Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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1
FIN630 Investment Analysis and Portfolio
Short Notes for Lecture 23-45
Prepared by Humera Fazal
INVESTMENT ANALYSIS amp PORTFOLIO MANAGEMENT (Dr Shahid A Zia)
Lecture No23
Random Walks Idea
bull Does not state that security prices move randomly
bull Rather it maintains that the news arrives randomly
bull And in accordance with the EMH security prices rapidly adjust to this random arrival of news
Consequences of Efficient Market
bull Quick price adjustment in response to the arrival of random information makes the reward for analysis
low
bull Prices reflect all available information
bull Price changes are independent of one another and move in a random fashion
ndash New information is independent of past
Evidence on Market Efficiency
bull Keys
ndash Consistency of returns in excess of risk
ndash Length of time over which returns are earned
bull Economically efficient markets
ndash Assets are priced so that investors cannot exploit any discrepancies and earn unusual returns
bull Transaction costs matter
Implications of Efficient Market Hypothesis
bull What should investors do if markets are efficient
bull Technical analysis
ndash Not valuable if the weak form holds
bull Fundamental analysis of intrinsic value
ndash Not valuable if semi-strong form holds
ndash Experience average results
bull For professional money managers
ndash Less time spent on individual securities
bull Passive investing favored
bull Otherwise must believe in superior insight
ndash Tasks if markets informationally efficient
bull Maintain correct diversification
bull Achieve and maintain desired portfolio risk
bull Manage tax burden
bull Control transaction costs
Market Anomalies
bull Exceptions that appear to be contrary to market efficiency
bull Earnings announcements affect stock prices
ndash Adjustment occurs before announcement but significant amount afterwards
ndash Contrary to efficient market because the lag should not exist
ndash The lag would than be a way of selling what you should bought earlier
ndash Extra returns than general public
bull Low PE ratio stocks tend to outperform high PE ratio stocks
ndash Low PE stocks generally have higher risk-adjusted returns
ndash But PE ratio is public information
bull Should portfolio be based on PE ratios
ndash Could result in an undiversified portfolio
bull Size effect
ndash Tendency for small firms to have higher risk-adjusted returns than large firms
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull January effect
ndash Tendency for small firm stock returns to be higher in January
ndash Of 30 size premium half of the effect occurs in January
bull Value Line Ranking System
ndash Advisory service that ranks 1000 stocks from best (1) to worst (5)
bull Probable price performance in next 12 months
ndash 13 years study (1980-1993) Group 1 stocks had annualized return of 19
bull Best investment letter performance overall
ndash Transaction costs may offset returns
Market Anomalies
bull Profitability ratios
bull Liquidity ratios
bull Business Sales ratios
Conclusions About Market Efficiency
bull Support for market efficiency is persuasive
ndash Much research using different methods
ndash Also many anomalies that cannot be explained satisfactorily
bull Markets very efficient but not totally
ndash To outperform the market fundamental analysis beyond the norm must be done
bull If markets operationally efficient some investors with the skill to detect a divergence between price and
semi-strong value earn profits
bull Controversy about the degree of market efficiency still remains
bull Excludes the majority of investors
bull Anomalies offer opportunities
Lecture No 24
Financial Research
bull Empirical Research
bull Theoretical Research
bull Behavioral Finance
Behavioral Finance
bull Seeks to integrate psychology into the investment process
bull A variety of established behavior patterns may influence security prices
bull If market is going bullish we will find that people are gathering behind the same sentiments and thinking
that the market is bullish whether it is or it isnrsquot become secondary
bull Our behavior is also a function of how a problem is framed and the reference point we use in evaluating
a situation
bull We may have definite preference for one alternative over another that according to classical finance is
economically equivalent
bull People get carried away with sentiments
Established Behaviors
bull Loss Aversion
bull Fear of Regret
bull Myopic Loss Aversion
bull Herding
bull Anchoring
bull Illusion of Control
bull Prospect Theory
bull Mental Accounting
bull Asset Segregation
bull Hindsight Bias
bull Overconfidence
bull Framing
bull Illusion of Truth
bull Biased Expectations
bull Reference Dependence
bull We also may misinterpret statistics especially by misjudging the likelihood of events
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Certain random numbers seem ―less random than others and this belief influences certain investment
decisions we might make
Mistaken Statistics
bull The Special Nature of Round Numbers
bull Extrapolation
bull Percentages vs Numbers
bull Apparent Order
bull Regression to the Mean
bull Sample Size
Risk Aversion
bull People tend to react differently when confronted with losses rather gains
bull There is a tendency to become less risk averse or even risk seeking when an adverse event occurs
bull Investors may choose to gamble on an even bigger loss in the hope that the loss will disappear
Equity Market Indicators
bull Provide a composite report of market behavior on a given day
bull Dow Jones Industrial Average (DJIA)
ndash Composed of 30 ―blue-chip stocks
ndash Price-weighted index Essentially adds the prices of 30 stocks divides by 30
bull Adjusted for stock splits stock dividends
ndash Oldest most well-known measure
bull Standard amp Poorrsquos Composite Index
ndash Composed of 500 ―large firm stocks
ndash Expressed as index number relative to a base index value of 10 (1941-43)
ndash Value-weighted index Prices and shares outstanding considered
bull Indicates how much the average equity value of the 500 firms in the index has increased
relative to the base period
bull NYSE and NASDAQ Composite Indices
ndash Value-weighted indices of broad markets
bull Nikkei 225 Average
ndash Price-weighted index of 225 actively-traded stocks on the Tokyo Stock Exchange
Index
bull Indexes are useful in assessing the performance of an investment
bull Choose which index
- It is important to ensure that the chosen index is an accurate proxy for what investors want to measure
- A stock index should not be used with a bond portfolio
- An index of large-capitalization stocks be used to judge a small-cap stock portfolio
bull An investor can choose from any of the hundreds of indexes
bull Equity securities
ndash Dow Jones Industrial Average (DJIA)
ndash SampP 500
bull Financial research
ndash SampP 500
Index Construction
bull Price Weighting
bull Equal Weighting
bull Capitalization Weighting
bull Volume based indices will tell you about companies that is best traded companies in the index
bull Price Weighting
- assigns heavy weight to high-priced stocks
- make use of a divisor to adjust for stock splits
bull The stocks in a way in which you would understand that if you have Rs 100 stock or Rs 500 stock and
Rs 10 stock or Rs 20 stock you would than give them you would than perhaps add them up and divide
by the number of stocks you want to based your indicator
bull Capitalization Weighting
- considers the size of the company
- needs no adjustment for stock splits
- must be adjusted for changes in
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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- index components
- primary stock offerings
- share repurchases
Few Indexes
bull ISE 10 index
bull LSE 25 index
bull KSE 100 index
LSE 25 INDEX
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
What is the KSE-100 Index
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
Lecture No 25
Popular Indexes
bull Stock Indexes
bull Bonds Indexes
bull Fixed Income Indexes
bull International Indexes
What is the KSE-100 Index
bull A benchmark of the Equity Market
bull 100 Stocks listed on KSE
bull Represents 80 percent of the total market
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
LSE 25 INDEX
bull LSE launched a new 25-Index on December 20 2002 which replaced the 101- IndexThe Index has a
Base Figure of 1000 (The Index closed at 544269 on 24th April 2006)
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
bull The Index was last reconstituted on July 1st 2006 in line with the regular review policy
bull KSE 100 is market capitalization based
bull LSE 25 is volume-based
Methods of Investing
bull Global Receipts
bull Country Funds
bull Individual Securities
bull Unit Investment Trusts
bull Local Mutual Fund
bull International Mutual Fund
bull Treasury bondsbills
Marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial paper
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull More risky than money market securities
bull Fixed-income securities have a specified payment schedule
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Dates and amount of interest and principal payments known in advance
Securitization
bull Transformation of illiquid non-marketable risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
bull Risk free profits
bull More riskier profit
bull Investing for short term
bull Investing for long term
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull Behaves like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull Common stockholders are residual claimants on income and assets
bull Par value is face value of a share
ndash Usually economically insignificant
bull Market value is more significant
bull Book value is accounting value of a share in case a company goes bankrupt
bull Dividends are cash payments to shareholders
ndash Dividend yield is income component of return =DP
ndash Payout Ratio is ratio of dividends to earnings
bull Stock dividend is payment to owners in stock
bull Stock split is the issuance of additional shares in proportion to the shares outstanding
ndash The book and par values are changed
bull PE ratio is the ratio of current market price of equity to the firmrsquos earnings
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase American Depository Receipts (ADRrsquos)
bull Issued by depositories having physical possession of foreign securities
bull Investors isolated from currency fluctuations
bull It means if there is a stock of an emerging markets people or investors in developed markets might not
be interested in investing in shares of an emerging market because of a fear of currency fluctuations
bull An asset back security product based on foreign currencies shares but traded in your own currency
Forms of Risks
bull Country Risks Sovereign Risks
bull Political Risks
bull Interest Rate Risks
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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6
bull Economic Risks
bull Regional Risks
bull Risk in specific company
bull Inflation Risks
In Upcoming Lecture
bull Bonds
bull Risk involved in trading
bull Portfolio
Lecture No 26
Bond Markets
bull Secondary bond market is primarily an over-the-counter network of dealers
ndash NYSE features an automated bond system to execute orders similar to SuperDot amp Instinet
bull Mostly corporate bonds thinly traded
ndash Treasury and agency bonds actively trade in dealers market
bull Municipal bonds local government bonds city bonds amp town bonds less actively traded
Bond Characteristics
bull Buyer of a newly issued coupon bond is lending money to the issuer who agrees to repay principal and
interest
bull Bonds are fixed-income securities
ndash Buyer knows future cash flows
ndash Known interest and principal payments
bull If sold before maturity price will depend on interest rates at that time
bull Prices quoted as a of par value
bull Bond buyer must pay the price of the bond plus accrued interest since last semiannual interest payment
ndash Prices quoted without accrued interest
ndash Premium payment
ndash Discount payment
bull Premium amount above par value
bull Discount amount below par value
Innovation in Bond Features
bull Zero-coupon bond
ndash Sold at a discount and redeemed for face value at maturity
ndash Locks in a fixed rate of return
ndash eliminating reinvestment rate risk
ndash Responds sharply to interest rate changes
Major Bond Types
bull Federal government securities (eg T-bonds)
bull Federal agency securities (eg GNMAs)
(Government National Mortgage Association)
bull Federally sponsored credit agency securities (eg FNMAs)
(Federal National Mortgage Association)
bull Municipal securities General obligation bonds Revenue bonds
Corporate Bonds
bull Usually unsecured debts maturing in 20-40 years paying semi-annual interest callable with par value
of $1000
ndash Callable bonds gives the issuer the right to repay the debt prior to maturity
ndash Convertible bonds may be exchanged for another asset at the ownerrsquos discretion
ndash Risk that issuer may default on payments
Bond Ratings
bull Rate relative probability of default
bull Rating organizations
ndash Standard and Poors Corporation (SampP)
ndash Moodyrsquos Investors Service Inc
bull Rating firms perform the credit analysis for the investor
bull Emphasis on the issuerrsquos relative probability of default
bull Investment grade securities
ndash Rated AAA
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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7
ndash AA
ndash A
ndash BBB
ndash Typically institutional investors are confined to bonds in these four categories
bull Speculative securities
ndash Rated BB
ndash B
ndash CCC
ndash CC
ndash C
ndash Significant uncertainties
ndash C rated bonds are not paying interest
Securitization
bull Transformation of illiquid risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull More like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull EPS
bull Dividend
bull Dividend Yield
bull Dividend Payout Ratio
bull PE Ratio
Lecture No 27
Alternative Investments Non-marketable Financial Assets
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial papers
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull Fixed-income securities have a specified payment schedule
ndash Dates and amount of interest and principal payments known in advance
bull More risky than money market securities
Alternative Investments Non-marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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8
Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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10
bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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11
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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12
bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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13
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
Prepared by Humera Fazal Channab College
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( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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Short Notes FIN 630 Chapters 23-45
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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26
Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Short Notes FIN 630 Chapters 23-45
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull January effect
ndash Tendency for small firm stock returns to be higher in January
ndash Of 30 size premium half of the effect occurs in January
bull Value Line Ranking System
ndash Advisory service that ranks 1000 stocks from best (1) to worst (5)
bull Probable price performance in next 12 months
ndash 13 years study (1980-1993) Group 1 stocks had annualized return of 19
bull Best investment letter performance overall
ndash Transaction costs may offset returns
Market Anomalies
bull Profitability ratios
bull Liquidity ratios
bull Business Sales ratios
Conclusions About Market Efficiency
bull Support for market efficiency is persuasive
ndash Much research using different methods
ndash Also many anomalies that cannot be explained satisfactorily
bull Markets very efficient but not totally
ndash To outperform the market fundamental analysis beyond the norm must be done
bull If markets operationally efficient some investors with the skill to detect a divergence between price and
semi-strong value earn profits
bull Controversy about the degree of market efficiency still remains
bull Excludes the majority of investors
bull Anomalies offer opportunities
Lecture No 24
Financial Research
bull Empirical Research
bull Theoretical Research
bull Behavioral Finance
Behavioral Finance
bull Seeks to integrate psychology into the investment process
bull A variety of established behavior patterns may influence security prices
bull If market is going bullish we will find that people are gathering behind the same sentiments and thinking
that the market is bullish whether it is or it isnrsquot become secondary
bull Our behavior is also a function of how a problem is framed and the reference point we use in evaluating
a situation
bull We may have definite preference for one alternative over another that according to classical finance is
economically equivalent
bull People get carried away with sentiments
Established Behaviors
bull Loss Aversion
bull Fear of Regret
bull Myopic Loss Aversion
bull Herding
bull Anchoring
bull Illusion of Control
bull Prospect Theory
bull Mental Accounting
bull Asset Segregation
bull Hindsight Bias
bull Overconfidence
bull Framing
bull Illusion of Truth
bull Biased Expectations
bull Reference Dependence
bull We also may misinterpret statistics especially by misjudging the likelihood of events
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bull Certain random numbers seem ―less random than others and this belief influences certain investment
decisions we might make
Mistaken Statistics
bull The Special Nature of Round Numbers
bull Extrapolation
bull Percentages vs Numbers
bull Apparent Order
bull Regression to the Mean
bull Sample Size
Risk Aversion
bull People tend to react differently when confronted with losses rather gains
bull There is a tendency to become less risk averse or even risk seeking when an adverse event occurs
bull Investors may choose to gamble on an even bigger loss in the hope that the loss will disappear
Equity Market Indicators
bull Provide a composite report of market behavior on a given day
bull Dow Jones Industrial Average (DJIA)
ndash Composed of 30 ―blue-chip stocks
ndash Price-weighted index Essentially adds the prices of 30 stocks divides by 30
bull Adjusted for stock splits stock dividends
ndash Oldest most well-known measure
bull Standard amp Poorrsquos Composite Index
ndash Composed of 500 ―large firm stocks
ndash Expressed as index number relative to a base index value of 10 (1941-43)
ndash Value-weighted index Prices and shares outstanding considered
bull Indicates how much the average equity value of the 500 firms in the index has increased
relative to the base period
bull NYSE and NASDAQ Composite Indices
ndash Value-weighted indices of broad markets
bull Nikkei 225 Average
ndash Price-weighted index of 225 actively-traded stocks on the Tokyo Stock Exchange
Index
bull Indexes are useful in assessing the performance of an investment
bull Choose which index
- It is important to ensure that the chosen index is an accurate proxy for what investors want to measure
- A stock index should not be used with a bond portfolio
- An index of large-capitalization stocks be used to judge a small-cap stock portfolio
bull An investor can choose from any of the hundreds of indexes
bull Equity securities
ndash Dow Jones Industrial Average (DJIA)
ndash SampP 500
bull Financial research
ndash SampP 500
Index Construction
bull Price Weighting
bull Equal Weighting
bull Capitalization Weighting
bull Volume based indices will tell you about companies that is best traded companies in the index
bull Price Weighting
- assigns heavy weight to high-priced stocks
- make use of a divisor to adjust for stock splits
bull The stocks in a way in which you would understand that if you have Rs 100 stock or Rs 500 stock and
Rs 10 stock or Rs 20 stock you would than give them you would than perhaps add them up and divide
by the number of stocks you want to based your indicator
bull Capitalization Weighting
- considers the size of the company
- needs no adjustment for stock splits
- must be adjusted for changes in
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- index components
- primary stock offerings
- share repurchases
Few Indexes
bull ISE 10 index
bull LSE 25 index
bull KSE 100 index
LSE 25 INDEX
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
What is the KSE-100 Index
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
Lecture No 25
Popular Indexes
bull Stock Indexes
bull Bonds Indexes
bull Fixed Income Indexes
bull International Indexes
What is the KSE-100 Index
bull A benchmark of the Equity Market
bull 100 Stocks listed on KSE
bull Represents 80 percent of the total market
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
LSE 25 INDEX
bull LSE launched a new 25-Index on December 20 2002 which replaced the 101- IndexThe Index has a
Base Figure of 1000 (The Index closed at 544269 on 24th April 2006)
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
bull The Index was last reconstituted on July 1st 2006 in line with the regular review policy
bull KSE 100 is market capitalization based
bull LSE 25 is volume-based
Methods of Investing
bull Global Receipts
bull Country Funds
bull Individual Securities
bull Unit Investment Trusts
bull Local Mutual Fund
bull International Mutual Fund
bull Treasury bondsbills
Marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial paper
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull More risky than money market securities
bull Fixed-income securities have a specified payment schedule
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ndash Dates and amount of interest and principal payments known in advance
Securitization
bull Transformation of illiquid non-marketable risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
bull Risk free profits
bull More riskier profit
bull Investing for short term
bull Investing for long term
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull Behaves like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull Common stockholders are residual claimants on income and assets
bull Par value is face value of a share
ndash Usually economically insignificant
bull Market value is more significant
bull Book value is accounting value of a share in case a company goes bankrupt
bull Dividends are cash payments to shareholders
ndash Dividend yield is income component of return =DP
ndash Payout Ratio is ratio of dividends to earnings
bull Stock dividend is payment to owners in stock
bull Stock split is the issuance of additional shares in proportion to the shares outstanding
ndash The book and par values are changed
bull PE ratio is the ratio of current market price of equity to the firmrsquos earnings
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase American Depository Receipts (ADRrsquos)
bull Issued by depositories having physical possession of foreign securities
bull Investors isolated from currency fluctuations
bull It means if there is a stock of an emerging markets people or investors in developed markets might not
be interested in investing in shares of an emerging market because of a fear of currency fluctuations
bull An asset back security product based on foreign currencies shares but traded in your own currency
Forms of Risks
bull Country Risks Sovereign Risks
bull Political Risks
bull Interest Rate Risks
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6
bull Economic Risks
bull Regional Risks
bull Risk in specific company
bull Inflation Risks
In Upcoming Lecture
bull Bonds
bull Risk involved in trading
bull Portfolio
Lecture No 26
Bond Markets
bull Secondary bond market is primarily an over-the-counter network of dealers
ndash NYSE features an automated bond system to execute orders similar to SuperDot amp Instinet
bull Mostly corporate bonds thinly traded
ndash Treasury and agency bonds actively trade in dealers market
bull Municipal bonds local government bonds city bonds amp town bonds less actively traded
Bond Characteristics
bull Buyer of a newly issued coupon bond is lending money to the issuer who agrees to repay principal and
interest
bull Bonds are fixed-income securities
ndash Buyer knows future cash flows
ndash Known interest and principal payments
bull If sold before maturity price will depend on interest rates at that time
bull Prices quoted as a of par value
bull Bond buyer must pay the price of the bond plus accrued interest since last semiannual interest payment
ndash Prices quoted without accrued interest
ndash Premium payment
ndash Discount payment
bull Premium amount above par value
bull Discount amount below par value
Innovation in Bond Features
bull Zero-coupon bond
ndash Sold at a discount and redeemed for face value at maturity
ndash Locks in a fixed rate of return
ndash eliminating reinvestment rate risk
ndash Responds sharply to interest rate changes
Major Bond Types
bull Federal government securities (eg T-bonds)
bull Federal agency securities (eg GNMAs)
(Government National Mortgage Association)
bull Federally sponsored credit agency securities (eg FNMAs)
(Federal National Mortgage Association)
bull Municipal securities General obligation bonds Revenue bonds
Corporate Bonds
bull Usually unsecured debts maturing in 20-40 years paying semi-annual interest callable with par value
of $1000
ndash Callable bonds gives the issuer the right to repay the debt prior to maturity
ndash Convertible bonds may be exchanged for another asset at the ownerrsquos discretion
ndash Risk that issuer may default on payments
Bond Ratings
bull Rate relative probability of default
bull Rating organizations
ndash Standard and Poors Corporation (SampP)
ndash Moodyrsquos Investors Service Inc
bull Rating firms perform the credit analysis for the investor
bull Emphasis on the issuerrsquos relative probability of default
bull Investment grade securities
ndash Rated AAA
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7
ndash AA
ndash A
ndash BBB
ndash Typically institutional investors are confined to bonds in these four categories
bull Speculative securities
ndash Rated BB
ndash B
ndash CCC
ndash CC
ndash C
ndash Significant uncertainties
ndash C rated bonds are not paying interest
Securitization
bull Transformation of illiquid risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull More like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull EPS
bull Dividend
bull Dividend Yield
bull Dividend Payout Ratio
bull PE Ratio
Lecture No 27
Alternative Investments Non-marketable Financial Assets
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial papers
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull Fixed-income securities have a specified payment schedule
ndash Dates and amount of interest and principal payments known in advance
bull More risky than money market securities
Alternative Investments Non-marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
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Short Notes FIN 630 Chapters 23-45
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8
Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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9
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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13
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
Prepared by Humera Fazal Channab College
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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31
ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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33
VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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34
ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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bull Certain random numbers seem ―less random than others and this belief influences certain investment
decisions we might make
Mistaken Statistics
bull The Special Nature of Round Numbers
bull Extrapolation
bull Percentages vs Numbers
bull Apparent Order
bull Regression to the Mean
bull Sample Size
Risk Aversion
bull People tend to react differently when confronted with losses rather gains
bull There is a tendency to become less risk averse or even risk seeking when an adverse event occurs
bull Investors may choose to gamble on an even bigger loss in the hope that the loss will disappear
Equity Market Indicators
bull Provide a composite report of market behavior on a given day
bull Dow Jones Industrial Average (DJIA)
ndash Composed of 30 ―blue-chip stocks
ndash Price-weighted index Essentially adds the prices of 30 stocks divides by 30
bull Adjusted for stock splits stock dividends
ndash Oldest most well-known measure
bull Standard amp Poorrsquos Composite Index
ndash Composed of 500 ―large firm stocks
ndash Expressed as index number relative to a base index value of 10 (1941-43)
ndash Value-weighted index Prices and shares outstanding considered
bull Indicates how much the average equity value of the 500 firms in the index has increased
relative to the base period
bull NYSE and NASDAQ Composite Indices
ndash Value-weighted indices of broad markets
bull Nikkei 225 Average
ndash Price-weighted index of 225 actively-traded stocks on the Tokyo Stock Exchange
Index
bull Indexes are useful in assessing the performance of an investment
bull Choose which index
- It is important to ensure that the chosen index is an accurate proxy for what investors want to measure
- A stock index should not be used with a bond portfolio
- An index of large-capitalization stocks be used to judge a small-cap stock portfolio
bull An investor can choose from any of the hundreds of indexes
bull Equity securities
ndash Dow Jones Industrial Average (DJIA)
ndash SampP 500
bull Financial research
ndash SampP 500
Index Construction
bull Price Weighting
bull Equal Weighting
bull Capitalization Weighting
bull Volume based indices will tell you about companies that is best traded companies in the index
bull Price Weighting
- assigns heavy weight to high-priced stocks
- make use of a divisor to adjust for stock splits
bull The stocks in a way in which you would understand that if you have Rs 100 stock or Rs 500 stock and
Rs 10 stock or Rs 20 stock you would than give them you would than perhaps add them up and divide
by the number of stocks you want to based your indicator
bull Capitalization Weighting
- considers the size of the company
- needs no adjustment for stock splits
- must be adjusted for changes in
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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4
- index components
- primary stock offerings
- share repurchases
Few Indexes
bull ISE 10 index
bull LSE 25 index
bull KSE 100 index
LSE 25 INDEX
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
What is the KSE-100 Index
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
Lecture No 25
Popular Indexes
bull Stock Indexes
bull Bonds Indexes
bull Fixed Income Indexes
bull International Indexes
What is the KSE-100 Index
bull A benchmark of the Equity Market
bull 100 Stocks listed on KSE
bull Represents 80 percent of the total market
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
LSE 25 INDEX
bull LSE launched a new 25-Index on December 20 2002 which replaced the 101- IndexThe Index has a
Base Figure of 1000 (The Index closed at 544269 on 24th April 2006)
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
bull The Index was last reconstituted on July 1st 2006 in line with the regular review policy
bull KSE 100 is market capitalization based
bull LSE 25 is volume-based
Methods of Investing
bull Global Receipts
bull Country Funds
bull Individual Securities
bull Unit Investment Trusts
bull Local Mutual Fund
bull International Mutual Fund
bull Treasury bondsbills
Marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial paper
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull More risky than money market securities
bull Fixed-income securities have a specified payment schedule
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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5
ndash Dates and amount of interest and principal payments known in advance
Securitization
bull Transformation of illiquid non-marketable risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
bull Risk free profits
bull More riskier profit
bull Investing for short term
bull Investing for long term
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull Behaves like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull Common stockholders are residual claimants on income and assets
bull Par value is face value of a share
ndash Usually economically insignificant
bull Market value is more significant
bull Book value is accounting value of a share in case a company goes bankrupt
bull Dividends are cash payments to shareholders
ndash Dividend yield is income component of return =DP
ndash Payout Ratio is ratio of dividends to earnings
bull Stock dividend is payment to owners in stock
bull Stock split is the issuance of additional shares in proportion to the shares outstanding
ndash The book and par values are changed
bull PE ratio is the ratio of current market price of equity to the firmrsquos earnings
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase American Depository Receipts (ADRrsquos)
bull Issued by depositories having physical possession of foreign securities
bull Investors isolated from currency fluctuations
bull It means if there is a stock of an emerging markets people or investors in developed markets might not
be interested in investing in shares of an emerging market because of a fear of currency fluctuations
bull An asset back security product based on foreign currencies shares but traded in your own currency
Forms of Risks
bull Country Risks Sovereign Risks
bull Political Risks
bull Interest Rate Risks
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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6
bull Economic Risks
bull Regional Risks
bull Risk in specific company
bull Inflation Risks
In Upcoming Lecture
bull Bonds
bull Risk involved in trading
bull Portfolio
Lecture No 26
Bond Markets
bull Secondary bond market is primarily an over-the-counter network of dealers
ndash NYSE features an automated bond system to execute orders similar to SuperDot amp Instinet
bull Mostly corporate bonds thinly traded
ndash Treasury and agency bonds actively trade in dealers market
bull Municipal bonds local government bonds city bonds amp town bonds less actively traded
Bond Characteristics
bull Buyer of a newly issued coupon bond is lending money to the issuer who agrees to repay principal and
interest
bull Bonds are fixed-income securities
ndash Buyer knows future cash flows
ndash Known interest and principal payments
bull If sold before maturity price will depend on interest rates at that time
bull Prices quoted as a of par value
bull Bond buyer must pay the price of the bond plus accrued interest since last semiannual interest payment
ndash Prices quoted without accrued interest
ndash Premium payment
ndash Discount payment
bull Premium amount above par value
bull Discount amount below par value
Innovation in Bond Features
bull Zero-coupon bond
ndash Sold at a discount and redeemed for face value at maturity
ndash Locks in a fixed rate of return
ndash eliminating reinvestment rate risk
ndash Responds sharply to interest rate changes
Major Bond Types
bull Federal government securities (eg T-bonds)
bull Federal agency securities (eg GNMAs)
(Government National Mortgage Association)
bull Federally sponsored credit agency securities (eg FNMAs)
(Federal National Mortgage Association)
bull Municipal securities General obligation bonds Revenue bonds
Corporate Bonds
bull Usually unsecured debts maturing in 20-40 years paying semi-annual interest callable with par value
of $1000
ndash Callable bonds gives the issuer the right to repay the debt prior to maturity
ndash Convertible bonds may be exchanged for another asset at the ownerrsquos discretion
ndash Risk that issuer may default on payments
Bond Ratings
bull Rate relative probability of default
bull Rating organizations
ndash Standard and Poors Corporation (SampP)
ndash Moodyrsquos Investors Service Inc
bull Rating firms perform the credit analysis for the investor
bull Emphasis on the issuerrsquos relative probability of default
bull Investment grade securities
ndash Rated AAA
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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7
ndash AA
ndash A
ndash BBB
ndash Typically institutional investors are confined to bonds in these four categories
bull Speculative securities
ndash Rated BB
ndash B
ndash CCC
ndash CC
ndash C
ndash Significant uncertainties
ndash C rated bonds are not paying interest
Securitization
bull Transformation of illiquid risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull More like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull EPS
bull Dividend
bull Dividend Yield
bull Dividend Payout Ratio
bull PE Ratio
Lecture No 27
Alternative Investments Non-marketable Financial Assets
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial papers
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull Fixed-income securities have a specified payment schedule
ndash Dates and amount of interest and principal payments known in advance
bull More risky than money market securities
Alternative Investments Non-marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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8
Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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9
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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10
bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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11
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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12
bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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13
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
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Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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28
bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
Prepared by Humera Fazal Channab College
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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4
- index components
- primary stock offerings
- share repurchases
Few Indexes
bull ISE 10 index
bull LSE 25 index
bull KSE 100 index
LSE 25 INDEX
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
What is the KSE-100 Index
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
Lecture No 25
Popular Indexes
bull Stock Indexes
bull Bonds Indexes
bull Fixed Income Indexes
bull International Indexes
What is the KSE-100 Index
bull A benchmark of the Equity Market
bull 100 Stocks listed on KSE
bull Represents 80 percent of the total market
bull Highest market capitalization in each of the 34 sectors
bull Largest market capitalization companies in descending order (66)
LSE 25 INDEX
bull LSE launched a new 25-Index on December 20 2002 which replaced the 101- IndexThe Index has a
Base Figure of 1000 (The Index closed at 544269 on 24th April 2006)
bull LSE 25-Index includes the top 25 traded companies at LSE and captures 53 of the market
capitalization and 98 of the total trading volume of LSE
bull The Index was last reconstituted on July 1st 2006 in line with the regular review policy
bull KSE 100 is market capitalization based
bull LSE 25 is volume-based
Methods of Investing
bull Global Receipts
bull Country Funds
bull Individual Securities
bull Unit Investment Trusts
bull Local Mutual Fund
bull International Mutual Fund
bull Treasury bondsbills
Marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial paper
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull More risky than money market securities
bull Fixed-income securities have a specified payment schedule
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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5
ndash Dates and amount of interest and principal payments known in advance
Securitization
bull Transformation of illiquid non-marketable risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
bull Risk free profits
bull More riskier profit
bull Investing for short term
bull Investing for long term
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull Behaves like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull Common stockholders are residual claimants on income and assets
bull Par value is face value of a share
ndash Usually economically insignificant
bull Market value is more significant
bull Book value is accounting value of a share in case a company goes bankrupt
bull Dividends are cash payments to shareholders
ndash Dividend yield is income component of return =DP
ndash Payout Ratio is ratio of dividends to earnings
bull Stock dividend is payment to owners in stock
bull Stock split is the issuance of additional shares in proportion to the shares outstanding
ndash The book and par values are changed
bull PE ratio is the ratio of current market price of equity to the firmrsquos earnings
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase American Depository Receipts (ADRrsquos)
bull Issued by depositories having physical possession of foreign securities
bull Investors isolated from currency fluctuations
bull It means if there is a stock of an emerging markets people or investors in developed markets might not
be interested in investing in shares of an emerging market because of a fear of currency fluctuations
bull An asset back security product based on foreign currencies shares but traded in your own currency
Forms of Risks
bull Country Risks Sovereign Risks
bull Political Risks
bull Interest Rate Risks
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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6
bull Economic Risks
bull Regional Risks
bull Risk in specific company
bull Inflation Risks
In Upcoming Lecture
bull Bonds
bull Risk involved in trading
bull Portfolio
Lecture No 26
Bond Markets
bull Secondary bond market is primarily an over-the-counter network of dealers
ndash NYSE features an automated bond system to execute orders similar to SuperDot amp Instinet
bull Mostly corporate bonds thinly traded
ndash Treasury and agency bonds actively trade in dealers market
bull Municipal bonds local government bonds city bonds amp town bonds less actively traded
Bond Characteristics
bull Buyer of a newly issued coupon bond is lending money to the issuer who agrees to repay principal and
interest
bull Bonds are fixed-income securities
ndash Buyer knows future cash flows
ndash Known interest and principal payments
bull If sold before maturity price will depend on interest rates at that time
bull Prices quoted as a of par value
bull Bond buyer must pay the price of the bond plus accrued interest since last semiannual interest payment
ndash Prices quoted without accrued interest
ndash Premium payment
ndash Discount payment
bull Premium amount above par value
bull Discount amount below par value
Innovation in Bond Features
bull Zero-coupon bond
ndash Sold at a discount and redeemed for face value at maturity
ndash Locks in a fixed rate of return
ndash eliminating reinvestment rate risk
ndash Responds sharply to interest rate changes
Major Bond Types
bull Federal government securities (eg T-bonds)
bull Federal agency securities (eg GNMAs)
(Government National Mortgage Association)
bull Federally sponsored credit agency securities (eg FNMAs)
(Federal National Mortgage Association)
bull Municipal securities General obligation bonds Revenue bonds
Corporate Bonds
bull Usually unsecured debts maturing in 20-40 years paying semi-annual interest callable with par value
of $1000
ndash Callable bonds gives the issuer the right to repay the debt prior to maturity
ndash Convertible bonds may be exchanged for another asset at the ownerrsquos discretion
ndash Risk that issuer may default on payments
Bond Ratings
bull Rate relative probability of default
bull Rating organizations
ndash Standard and Poors Corporation (SampP)
ndash Moodyrsquos Investors Service Inc
bull Rating firms perform the credit analysis for the investor
bull Emphasis on the issuerrsquos relative probability of default
bull Investment grade securities
ndash Rated AAA
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Short Notes FIN 630 Chapters 23-45
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7
ndash AA
ndash A
ndash BBB
ndash Typically institutional investors are confined to bonds in these four categories
bull Speculative securities
ndash Rated BB
ndash B
ndash CCC
ndash CC
ndash C
ndash Significant uncertainties
ndash C rated bonds are not paying interest
Securitization
bull Transformation of illiquid risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull More like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull EPS
bull Dividend
bull Dividend Yield
bull Dividend Payout Ratio
bull PE Ratio
Lecture No 27
Alternative Investments Non-marketable Financial Assets
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial papers
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull Fixed-income securities have a specified payment schedule
ndash Dates and amount of interest and principal payments known in advance
bull More risky than money market securities
Alternative Investments Non-marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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8
Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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9
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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10
bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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11
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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12
bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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13
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
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bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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24
bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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Short Notes FIN 630 Chapters 23-45
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Dates and amount of interest and principal payments known in advance
Securitization
bull Transformation of illiquid non-marketable risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
bull Risk free profits
bull More riskier profit
bull Investing for short term
bull Investing for long term
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull Behaves like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull Common stockholders are residual claimants on income and assets
bull Par value is face value of a share
ndash Usually economically insignificant
bull Market value is more significant
bull Book value is accounting value of a share in case a company goes bankrupt
bull Dividends are cash payments to shareholders
ndash Dividend yield is income component of return =DP
ndash Payout Ratio is ratio of dividends to earnings
bull Stock dividend is payment to owners in stock
bull Stock split is the issuance of additional shares in proportion to the shares outstanding
ndash The book and par values are changed
bull PE ratio is the ratio of current market price of equity to the firmrsquos earnings
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase American Depository Receipts (ADRrsquos)
bull Issued by depositories having physical possession of foreign securities
bull Investors isolated from currency fluctuations
bull It means if there is a stock of an emerging markets people or investors in developed markets might not
be interested in investing in shares of an emerging market because of a fear of currency fluctuations
bull An asset back security product based on foreign currencies shares but traded in your own currency
Forms of Risks
bull Country Risks Sovereign Risks
bull Political Risks
bull Interest Rate Risks
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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6
bull Economic Risks
bull Regional Risks
bull Risk in specific company
bull Inflation Risks
In Upcoming Lecture
bull Bonds
bull Risk involved in trading
bull Portfolio
Lecture No 26
Bond Markets
bull Secondary bond market is primarily an over-the-counter network of dealers
ndash NYSE features an automated bond system to execute orders similar to SuperDot amp Instinet
bull Mostly corporate bonds thinly traded
ndash Treasury and agency bonds actively trade in dealers market
bull Municipal bonds local government bonds city bonds amp town bonds less actively traded
Bond Characteristics
bull Buyer of a newly issued coupon bond is lending money to the issuer who agrees to repay principal and
interest
bull Bonds are fixed-income securities
ndash Buyer knows future cash flows
ndash Known interest and principal payments
bull If sold before maturity price will depend on interest rates at that time
bull Prices quoted as a of par value
bull Bond buyer must pay the price of the bond plus accrued interest since last semiannual interest payment
ndash Prices quoted without accrued interest
ndash Premium payment
ndash Discount payment
bull Premium amount above par value
bull Discount amount below par value
Innovation in Bond Features
bull Zero-coupon bond
ndash Sold at a discount and redeemed for face value at maturity
ndash Locks in a fixed rate of return
ndash eliminating reinvestment rate risk
ndash Responds sharply to interest rate changes
Major Bond Types
bull Federal government securities (eg T-bonds)
bull Federal agency securities (eg GNMAs)
(Government National Mortgage Association)
bull Federally sponsored credit agency securities (eg FNMAs)
(Federal National Mortgage Association)
bull Municipal securities General obligation bonds Revenue bonds
Corporate Bonds
bull Usually unsecured debts maturing in 20-40 years paying semi-annual interest callable with par value
of $1000
ndash Callable bonds gives the issuer the right to repay the debt prior to maturity
ndash Convertible bonds may be exchanged for another asset at the ownerrsquos discretion
ndash Risk that issuer may default on payments
Bond Ratings
bull Rate relative probability of default
bull Rating organizations
ndash Standard and Poors Corporation (SampP)
ndash Moodyrsquos Investors Service Inc
bull Rating firms perform the credit analysis for the investor
bull Emphasis on the issuerrsquos relative probability of default
bull Investment grade securities
ndash Rated AAA
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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7
ndash AA
ndash A
ndash BBB
ndash Typically institutional investors are confined to bonds in these four categories
bull Speculative securities
ndash Rated BB
ndash B
ndash CCC
ndash CC
ndash C
ndash Significant uncertainties
ndash C rated bonds are not paying interest
Securitization
bull Transformation of illiquid risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull More like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull EPS
bull Dividend
bull Dividend Yield
bull Dividend Payout Ratio
bull PE Ratio
Lecture No 27
Alternative Investments Non-marketable Financial Assets
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial papers
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull Fixed-income securities have a specified payment schedule
ndash Dates and amount of interest and principal payments known in advance
bull More risky than money market securities
Alternative Investments Non-marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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8
Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
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Short Notes FIN 630 Chapters 23-45
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bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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10
bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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11
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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36
bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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Short Notes FIN 630 Chapters 23-45
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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Short Notes FIN 630 Chapters 23-45
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bull Economic Risks
bull Regional Risks
bull Risk in specific company
bull Inflation Risks
In Upcoming Lecture
bull Bonds
bull Risk involved in trading
bull Portfolio
Lecture No 26
Bond Markets
bull Secondary bond market is primarily an over-the-counter network of dealers
ndash NYSE features an automated bond system to execute orders similar to SuperDot amp Instinet
bull Mostly corporate bonds thinly traded
ndash Treasury and agency bonds actively trade in dealers market
bull Municipal bonds local government bonds city bonds amp town bonds less actively traded
Bond Characteristics
bull Buyer of a newly issued coupon bond is lending money to the issuer who agrees to repay principal and
interest
bull Bonds are fixed-income securities
ndash Buyer knows future cash flows
ndash Known interest and principal payments
bull If sold before maturity price will depend on interest rates at that time
bull Prices quoted as a of par value
bull Bond buyer must pay the price of the bond plus accrued interest since last semiannual interest payment
ndash Prices quoted without accrued interest
ndash Premium payment
ndash Discount payment
bull Premium amount above par value
bull Discount amount below par value
Innovation in Bond Features
bull Zero-coupon bond
ndash Sold at a discount and redeemed for face value at maturity
ndash Locks in a fixed rate of return
ndash eliminating reinvestment rate risk
ndash Responds sharply to interest rate changes
Major Bond Types
bull Federal government securities (eg T-bonds)
bull Federal agency securities (eg GNMAs)
(Government National Mortgage Association)
bull Federally sponsored credit agency securities (eg FNMAs)
(Federal National Mortgage Association)
bull Municipal securities General obligation bonds Revenue bonds
Corporate Bonds
bull Usually unsecured debts maturing in 20-40 years paying semi-annual interest callable with par value
of $1000
ndash Callable bonds gives the issuer the right to repay the debt prior to maturity
ndash Convertible bonds may be exchanged for another asset at the ownerrsquos discretion
ndash Risk that issuer may default on payments
Bond Ratings
bull Rate relative probability of default
bull Rating organizations
ndash Standard and Poors Corporation (SampP)
ndash Moodyrsquos Investors Service Inc
bull Rating firms perform the credit analysis for the investor
bull Emphasis on the issuerrsquos relative probability of default
bull Investment grade securities
ndash Rated AAA
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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7
ndash AA
ndash A
ndash BBB
ndash Typically institutional investors are confined to bonds in these four categories
bull Speculative securities
ndash Rated BB
ndash B
ndash CCC
ndash CC
ndash C
ndash Significant uncertainties
ndash C rated bonds are not paying interest
Securitization
bull Transformation of illiquid risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull More like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull EPS
bull Dividend
bull Dividend Yield
bull Dividend Payout Ratio
bull PE Ratio
Lecture No 27
Alternative Investments Non-marketable Financial Assets
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial papers
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull Fixed-income securities have a specified payment schedule
ndash Dates and amount of interest and principal payments known in advance
bull More risky than money market securities
Alternative Investments Non-marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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9
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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11
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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33
VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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34
ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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ndash AA
ndash A
ndash BBB
ndash Typically institutional investors are confined to bonds in these four categories
bull Speculative securities
ndash Rated BB
ndash B
ndash CCC
ndash CC
ndash C
ndash Significant uncertainties
ndash C rated bonds are not paying interest
Securitization
bull Transformation of illiquid risky individual loans into asset-backed securities
ndash GNMAs
ndash Marketable securities backed by auto loans credit-card receivables small-business loans leases
bull High yields short maturities investment-grade ratings
Equity Securities
bull Denote an ownership interest in a corporation
bull Denote control over management at least in principle
ndash Voting rights important
bull Denote limited liability
ndash Investor cannot lose more than their investment should the corporation fail
Preferred Stocks
bull More like bonds
bull Hybrid security because features of both debt and equity
bull Preferred stockholders paid after debt but before common stockholders
ndash Dividend known fixed in advance
ndash May be cumulative if dividend omitted
bull Often convertible into common stock
bull May carry variable dividend rate
Common Stocks
bull EPS
bull Dividend
bull Dividend Yield
bull Dividend Payout Ratio
bull PE Ratio
Lecture No 27
Alternative Investments Non-marketable Financial Assets
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Money Market Securities
bull Marketable claims are negotiable or salable in the marketplace
bull Short-term liquid relatively low risk debt instruments
bull Issued by governments and private firms
bull Examples Money market mutual funds
T-Bills Commercial papers
Capital Market Securities
bull Marketable debt with maturity greater than one year and ownership shares
bull Fixed-income securities have a specified payment schedule
ndash Dates and amount of interest and principal payments known in advance
bull More risky than money market securities
Alternative Investments Non-marketable Financial Assets
bull Commonly owned by individuals
bull Represent direct exchange of claims between issuer and investor
bull Usually very liquid or easy to convert to cash without loss of value
bull Examples Savings accounts and bonds certificates of deposit money market deposit accounts
Prepared by Humera Fazal Channab College
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Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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9
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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13
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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32
ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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33
VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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34
ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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Derivative Securities
bull Securities whose value is derived from another security or derived from an underlying assets
bull Futures and options contracts are standardized and performance is guaranteed by a third party
bull Warrants are options issued by firms
bull Risk management tools
Market Mechanics
bull Regular Markets
bull Spot Markets
bull Original Markets
bull Future Markets
Options
bull Exchange-traded options are created by investors not corporations
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Right is sold in the market at a price
bull Increases return possibilities
bull Chicago Board of Auction Exchange
Derivatives
bull Warrants
bull Options
bull SWOPS
Futures
bull Futures contract A standardized agreement between a buyer and seller to make future delivery of a
fixed asset at a fixed price
ndash A ―good faith deposit called margin is required of both the buyer and seller to reduce default
risk
ndash Used to hedge the risk of price changes
Bond Fundamentals Bond Principles
bull Identification of Bonds
bull Classification of Bonds
bull Terms of Repayment
bull Bond Cash Flows
bull Convertible and Exchangeable Bonds
bull Registration
bull Bonds are identified by
- Issuers
- Coupon
- Maturity Year
Who is behind the Bond Issuer
Coupon Rate
Maturity Period
Classification of Bonds
bull Bonds are classified according to
- the nature of the issuer
- Security behind the bonds
- Some bonds provide a conversion feature
- exchanged for another asset
- usually shares of common stock in the
issuing companies
- The bond indenture spells out the details
Terms of Repayment
bull The income stream associated with most bonds contains
ndash an annuity stream
ndash a single sum to be received in the future
ndash Semi-annual
bull Bond Pricing amp Returns
bull Valuation Equations
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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9
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
Prepared by Humera Fazal Channab College
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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33
VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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34
ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Dividend Reinvestment Program
Yield to maturity
bull The discount rate that equates the present value of the future cash flows with the current price of the
bond
bull By tradition bond yield to maturity is based on semiannual compounding
Bond Cash Flows
bull A major assumption of the yield to maturity calculation
- the requirement that coupon proceeds be reinvested at the bondrsquos yield to maturity
bull If the reinvestment rate is different from the bondrsquos rate the rate of return ultimately realized will be
different
Example
Return of Bond
bull When comparing bonds with other investments the effective annual yield (realized compound yield)
should be used to make a realistic comparison
bull The yield curve shows the relationship between yield and time until maturity
bull Bonds accrue interest each day they are held
Bond Prices
bull Bond prices are expressed as a percentage of par value
bull Corporate bonds usually trade in minimum price increments of 18
bull Government bonds trade in 132nds
Lecture No 28
Investing Internationally
bull Direct investing
ndash US stockbrokers can buy and sell securities on foreign stock exchanges
ndash Foreign firms may list their securities on a US exchange or on NASDAQ
ndash Purchase ADRrsquos
ndash Purchase GDRrsquos
Derivative Securities
bull Securities whose value is derived from another security
bull Futures and options contracts are standardized and performance is guaranteed by a third party
ndash Risk management tools
bull Warrants are options issued by firms
Bond Pricing amp Returns
bull Valuation Equations
bull Yield to Maturity
bull Spot Rates
bull Realized Compound Yield
bull Current Yield
bull Accrued Interest
Bond Risks
Price Risks
bull Price Risks Refer to the chance of monetary loss due to
1 default risk
The likelihood of the firm defaulting on its loan repayments
2 interest rate risk
The variability of interest rates
Sovereign Risk
Convenience Risks
bull Refer to additional demands on management time because of
- Bonds being called by their issuers
- The need to reinvest interest received
- Poor marketability of a particular issue
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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11
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
Prepared by Humera Fazal Channab College
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
Prepared by Humera Fazal Channab College
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
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35
ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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bull May bonds have a period of call protection and subsequently a declining call premium
Bonds
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term riskless rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
ndash Other rates differ because of
bull Maturity differentials
bull Security risk premiums
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade investors to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
Determinants of Interest Rates
bull Market interest rates on interest debt
bull real rate + expected inflation
ndash Fisher Hypothesis
ndash Real Estate
bull Real rate estimates obtained by subtracting the expected inflation rate from the observed nominal rate
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull Long-term bonds tend to be more price sensitive than short-term bonds
bull The relationships with respect to maturity are not exact as they are when duration is used
bull In discussing the pricing relationships it is helpful to discuss how maturity and cash flows as measured
by coupon rates must be considered to get exact relationships
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
Yield to Maturity
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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11
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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12
bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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24
bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
ndash Rates will vary
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
ndash Required to compute intrinsic value
bull Expected cash flows
bull Timing of expected cash flows
bull Discount rate or required rate of return by investors
Bond Valuation
bull Value of a coupon bond
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with same maturity and credit
risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
Bond Price Changes
bull Holding maturity constant a rate decrease will raise prices a greater percentage than a corresponding
increase in rates will lower prices
Lecture 29
Bond Risks
Price Risks
bull Interest Rate Risk
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
01
21
ndrice of boPurchase p
re dollarsTotal futu RCY
n
n
n
tt
t
)r(
MV
)r(
C V
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
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bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
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Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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Short Notes FIN 630 Chapters 23-45
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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24
bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
Prepared by Humera Fazal Channab College
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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Short Notes FIN 630 Chapters 23-45
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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Short Notes FIN 630 Chapters 23-45
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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Short Notes FIN 630 Chapters 23-45
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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Short Notes FIN 630 Chapters 23-45
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Default Risk
bull Price Risks Refer to the chance of monetary loss due to
1 Default Risk
The likelihood of the firm defaulting on its loan payments
2 Interest Rate Risk
The variability of interest rates
Convenience Risks
bull Refer to additional demands on management time because of
- bonds being called by their issuers
- the need to reinvest interest received
bull May bonds have a period of call protection and subsequently a declining call premium
bull Poor marketability of a particular issue
Interest Rates
bull Rates and basis points
ndash 100 basis points are equal to one percentage point
bull Short-term risk less rate
ndash Provides foundation for other rates
ndash Approximated by rate on Treasury bills
bull Maturity differentials
ndash Term structure of interest rates
bull Accounts for the relationship between time and yield for bonds the same in every other
respect
bull Risk premium
ndash Yield spread or yield differential
ndash Associated with issuerrsquos particular situation
Determinants of Interest Rates
bull Real rate of interest
ndash Rate that must be offered to persuade individuals to save rather than consume
ndash Rate at which real capital physically reproduces itself
bull Nominal interest rate
ndash Function of the real rate of interest and expected inflation premium
bull Market interest rates on risk less debt real rate +expected inflation
ndash Fisher Hypothesis
Bond Pricing Relationships
bull Inverse relationship between price and yield
bull An increase in a bondrsquos yield to maturity results in a smaller price decline than the gain associated with
a decrease in yield
bull As maturity increases price sensitivity increases at a decreasing rate
bull Price sensitivity is inversely related to a bondrsquos coupon rate
bull Price sensitivity is inversely related to the yield to maturity at which the bond is selling
Measuring Bond Yields
bull Yield to maturity
ndash Most commonly used
ndash Promised compound rate of return received from a bond purchased at the current market price
and held to maturity
ndash Equates the present value of the expected future cash flows to the initial investment
bull Similar to internal rate of return
bull Solve for YTM
ndash For a zero coupon bond
bull Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM
1[MVP]2YTM 12n
n
n
tt
t
)YTM(
MV
)YTM(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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13
Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
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Short Notes FIN 630 Chapters 23-45
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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30
bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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31
ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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32
ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
Prepared by Humera Fazal Channab College
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
Prepared by Humera Fazal Channab College
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Yield to Call
bull Yield based on the deferred call period
bull Substitute number of periods until first call date for and call price for face value
Realized Compound Yield
bull Rate of return actually earned on a bond given the reinvestment of the coupons at varying rates
bull Horizon return analysis
ndash Bond returns based on assumptions about reinvestment rates
Bond Valuation Principle
bull Intrinsic value
ndash An estimated value
ndash Present value of the expected cash flows
bull Expected cash flows
bull Ratings
bull Timing of expected cash flows
Bond Valuation
bull Value of a coupon bond
Formula
bull Biggest problem is determining the discount rate or required yield
bull Required yield is the current market rate earned on comparable bonds with in the same maturity and
credit risk
Bond Price Changes
bull Over time bond prices that differ from face value must change
bull Bond prices move inversely to market yields
bull The change in bond prices due to a yield change is directly related to time to maturity and indirectly
related to coupon rate
bull Holding maturity constant a rate decrease will raise prices a greater percent than a corresponding
increase in rates will lower prices
Measuring Bond Price Volatility Duration
bull Important considerations
ndash Different effects of yield changes on the prices and rates of return for different bonds
ndash Maturity
ndash It May not have an identical economic lifetime
ndash A measure is needed that accounts for both size and timing of cash flows
ndash Maturity is an inadequate measure of volatility
What is Duration
bull It is a measure of a bondrsquos lifetime stated in years that accounts for the entire pattern (both size and
timing) of the cash flows over the life of the bond
bull The weighted average maturity of a bondrsquos cash flows
ndash Weights determined by present value of cash flows
bull A measure of the effective maturity of a bond
bull The weighted average of the time until each payment is received with the weights proportional to the
present value of the payment
bull Duration is shorter than maturity for all bonds except zero coupon bonds
bull Duration is equal to maturity for zero coupon bonds
Price
Market yield
c
c
tt
t
)YTC(
CP
)YTC(
C P
2
2
1 2121
2
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Short Notes FIN 630 Chapters 23-45
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14
bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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37
bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull The description of duration that is used here stresses the concept of average life
bull Since the measurement of duration considers the timing and value of intermediate payments
bull It is an accurate measure of average life and is more meaningful that maturity for any bond than has
coupon payments
Why is Duration Important
bull It allows comparison of effective lives of bonds that differ in maturity coupon
bull It is used in bond management strategies particularly immunization
bull Measures bond price sensitivity to interest rate movements which is very important in any bond
analysis
DurationPrice Relationship
bull Price change is proportional to duration and not to maturity
bull One of the key properties of duration is related to price changes
bull Price changes on fixed-income securities are proportional to duration
bull Duration incorporates both the coupon rate and maturity effects into a single measure
bull The concept of modified duration is used extensively in industry
Duration
bull Duration is an average signifying the point in time when the PV of a security is repaid
bull A measure of the price sensitivity of a security to interest rate changes
bull ( P ) P = - D x ( i ) ( 1 + i ) ~ - D i
bull Measure of bond volatility
bull Holding period sufficient to balance price and reinvestment risk assuring the investor the yield to
maturity
bull Ratio of sum of discounted time weighted CF divided by price of security
bull Duration values change each day
bull Measure of interest rate risk
bull as measure of bond volatility
bull Inversely related to coupon rate amp current market rate of return
bull More refined measure of maturity that helps determine how much more risk there is
bull Weighted average of time it takes to recoup your investment - counts interest (coupon) payments as well
as principal payment
bull Each payment is discounted in terms of its PV
bull For zero coupon bonds duration = maturity - get all CF at maturity
bull Key concepts
bull The longer the maturity of a bond (other things equal) the greater its price volatility
bull The smaller the coupon of the bonds (other things equal) the greater its Duration amp the greater its price
sensitivity (volatility)
bull Duration is a positive function of term to maturity amp a negative function of size of the coupon of the
bond (extremely low coupon - zero coupon duration = maturity)
bull Numerator is PV of all cash flows weighted according to length of time to receipt
bull Denominator = PV of cash flows = Price
bull For zero coupon security duration = maturity
bull With longer duration need a larger price change to get same yield change - can see that in Treasury
Bond Note amp Bill column 30-year bond fell ( 10 32 ) on 71698 while 2 yr note fell only (1 32)
Uses of Duration
bull Maturity Matching approach
bull Zero coupon approach
bull Duration-Matching approach
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
bull Duration is a measure of interest rate risk that considers the effects of both the coupon rate amp maturity
changes in bond prices
bull By matching the duration of their firmrsquos assets amp liabilities managers of financial institutions can
minimize exposure to interest rate risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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15
bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
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The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
Prepared by Humera Fazal Channab College
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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Short Notes FIN 630 Chapters 23-45
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
Prepared by Humera Fazal Channab College
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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28
bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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30
bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
Prepared by Humera Fazal Channab College
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
Prepared by Humera Fazal Channab College
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
Prepared by Humera Fazal Channab College
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
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bull Duration is the figure that we need to look at when we talking about being able to measure interest rate
risk and by looking at the duration will be able to avoid the effect of interest rate risk on our realized
rates of return
bull Immunization of interest rate risk is a tool that can be used for passive management
bull Financial institutions use immunization concept to manage assets and liabilities
bull To control for interest rate risk managers of financial institutions balance the durations of their asset and
liability portfolios
bull Target date immunization can be used to lock in a fixed rate of return for some investment horizon
Duration problem
Example
bull Example $100 par 6 coupon 5 years (10 semi-annual payments of 3 each six months) in an
8 market ( 4 semi-annual yield)
Per (n) CF DF PV of CF n x PV of CF
1 $ 30 9615 28845 28845
2 30 9246 27738 55476
3 30 8890 2667 8001
4 30 8548 25664 102576
5 30 8219 24657 123285
helliphelliphelliphellip
10 1030 6756 698568 698568
Per (n) CF DF PV of CF nx PV of
CF
1 3 09615 28845 28845
2 3 09246 27738 55476
3 3 0889 2667 8001
4 3 08548 25644 102576
5 3 08219 24657 123285
6 3 07903 23709 142254
7 3 07599 22797 159579
8 3 07307 21921 175368
9 3 07026 21078 189702
10 103 06756 698568 698568
Sum PV amp weighted PV column 918927 8015775
bull Duration of this security = 8015775 918927 = 87229726 half years
bull = 436 years
bull So the five year 6 coupon security has a duration of 436 years in a market where expected yield to
maturity = 8
bull Find duration if i = 4
bull Is it the same as when i = 8 (hint no)
bull Modified duration = duration (1 + i )
Lecture 30
Rules for Duration
bull Rule 1 The duration of a zero-coupon bond equals its time to maturity
bull Rule 2 Holding maturity constant a bondrsquos duration is higher when the coupon rate is lower
bull Rule 3 Holding the coupon rate constant a bondrsquos duration generally increases with its time to maturity
bull Rule 4 Holding other factors constant the duration of a coupon bond is higher when the bondrsquos yield to
maturity is lower
Duration Conclusions
bull To obtain maximum price volatility investors should choose bonds with the longest duration
bull Duration is additive
ndash Portfolio duration is just a weighted average
Prepared by Humera Fazal Channab College
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16
bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
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Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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24
bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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37
bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
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bull Duration measures volatility which isnrsquot the only aspect of risk in bonds
bull Default risk in bonds
bull Interest rate risks in bonds
Convexity
bull Convexity is very important consideration in the bond market
bull Significance of convexity
Convexity
bull Refers to the degree to which duration changes as the yield to maturity changes
ndash Price-yield relationship is convex
bull Duration equation assumes a linear relationship between price and yield
bull Convexity largest for low coupon long-maturity bonds and low yield to maturity
Pricing Error from Convexity
Bond price volatility
bull Bond prices are inversely related to bond yields
bull The price volatility of a long-term bond is greater than that of a short-term bond holding the coupon rate
constant
bull The price volatility of a low-coupon bond is greater than that of a high-coupon bond holding maturity
constant
Example of Bond volatility
bull The price of a 2-year bond (with one year remaining - so really a 1-year bond) fell by 957 when
market yield increased from 5 to 6 and rose by 971 when market yields fell from 5 to 4
bull This measure of percentage price change is called bond volatility
bull What if we had a bond with 30 years remaining amp a 5 coupon and market rates rose to 6
bull Again assume semi-annual coupons of 25 when market semi-annual yields are 3
Bond volatility
bull P = 25(103) + 25(103)2 + 25(103)3 + 25(103)4 + 25(103)5 + 25(103)30 + 1000(103)30
= 2427 + 2356 + 2288 + + 424 + 16973 = 86162
bull What is the percentage change in price
bull P = (86162-1000)1000 = - 981000 = - 138
bull For the same change in yield (from 5 to 6) the 1-year security had a 957 change in price amp the 30-
year security had a 138 change in price
Bond price volatility
bull Bond price volatility is the percentage change in bond price for a given change in yield
bull Volatility increases with maturity
bull A 1 increase in market yields from 5 gives volatility of
bull 1 year - 957 (price fell to 99043)
bull 15 year - 98 (price fell to 902)
bull 30 year - 138 (price fell to 86162)
Zero Coupon
bull What is the volatility of a 30-year zero coupon bond if market rates change from 5 to 6
bull P0 = 1000 (105)30 = 23138
bull P1 = 1000 (106)30 = 17411
bull P = (17411 - 23138)23138 = - 329
bull Conclusion lower coupon has more volatility
Price
Yield
Duratio
n
Pricing Error from
Convexity
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Short Notes FIN 630 Chapters 23-45
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( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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Short Notes FIN 630 Chapters 23-45
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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30
bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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31
ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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32
ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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33
VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
Prepared by Humera Fazal Channab College
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
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17
( - 329 vs -138 for 5 coupon)
bull If assume 60-semi annual compounding periods with c = I = 25 P0 = 1000 (1025)60 = 22728
bull or P1 = 1000 (103)60 = 16973
bull P = (16973 - 22728)22728 = - 339
Summary
bull Bond prices are inversely related to bond yields
bull The price volatility of a longer-maturity security is larger than that of a shorter maturity security
holding the coupon rate constant
bull The price volatility of a low coupon security is larger than that of a high coupon security holding
maturity constant
bull IRR (Interest rate risk) occurs when realized return doesnrsquot = YTM
ndash Why does this happen How can it be avoided
What does the price volatility of a bond depend on
1 Maturity
2 Coupon
3 Yield to maturity
Approximate change in price of bond
bull To get a approximate change in the price of a bond for a change in yield we just multiply it by the
change in yield
bull This is a linear approximation good for small change in interest rates
Lecture 31
Bonds
bull So now youve learned the basics of bonds Not too complicated was it
bull Here is a recap of what we discussed
bull Bonds are just like IOUs
bull Buying a bond means you are lending out your money
bull Bonds are also called fixed-income securities because the cash flow from them is fixed
bull Stocks are equity bonds are debt
bull Issuers of bonds are governments and corporations
bull A bond is characterized by its face value coupon rate maturity and issuer
bull Yield is the rate of return you get on a bond
bull When price goes up yield goes down and vice versa
bull Interest Rates
bull When interest rates rise the price of bonds in the market falls
bull When interest rates go down the price of bonds in the market rise
bull Bills notes and bonds are all fixed-income securities classified by maturity
bull Government bonds are the safest followed by municipal bonds and then corporate bonds
bull Bonds are not risk free Its always possible especially for corporate bonds for the borrower to default
on the debt payments
bull High risk high yield bonds are known as junk bonds
Understanding
Risk and Return
bull Two key concepts in Finance are
ndash The time value for money
ndash The fact that a safe rupee is worth more than a risky rupee
bull The trade-off is the central theme in the investment decision-making process
Return
bull Holding Period Return
bull Yield and Appreciation
bull Compounding
bull Compound Annual Return
bull Simple interest returns
Holding Period Return
bull Independent of the passage of time
bull Should only be used to compare investments over identical time periods
bull Consider the yield of an investment from interest or dividends
bull Consider the appreciation from a chance in the investment value
Prepared by Humera Fazal Channab College
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
Prepared by Humera Fazal Channab College
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The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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21
TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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22
ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
Prepared by Humera Fazal Channab College
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24
bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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26
Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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28
bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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29
ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
Prepared by Humera Fazal Channab College
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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18
Supplement Their Income
bull Returns in the form of Interest
bull Returns in the form of Dividend
Time Value of Money
bull Its calculations over come the shortcomings of the holding period return
bull Permit a direct comparison between a particular sum today and amounts in the future
bull Inflation
bull Worth investing or not
bull Compound annual return - the interest rate that satisfies a time value of money equation
bull The number of compound periods per year can significantly increase the compound annual return
bull Semi-annual coupon rates
bull Twice in year payments
bull Multiples of coupon rates
bull Purchase of bond in January
bull Purchase of bond in April
Hypothetical Assumption
bull 2 biannual or semi-annual return
bull 4 quarterly returns to be reinvested
Risk
bull A chance of loss
bull Inseparable from time
bull Breakeven ndash the point decide gain or loss
bull Virtually all investors are risk averse especially with significant sums of money Total risk ndash complete
variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Breakeven
bull Cost
ndash Manufacturing cost
ndash Financial cost
ndash Administrative cost
ndash Marketing cost
Factors
bull Greed
bull Fear
Junk Bonds
Risk
bull Total risk is complete variability of investment results
bull Total risk can be partitioned into diversifiable and un-diversifiable risk
bull The marketplace only rewards un-diversifiable risk
bull No Pain No Gain
bull Risk is unavoidable
bull A direct relationship between expected return and unavoidable risk
bull Risk investment doesnrsquot guarantee a return
bull Unnecessary risk doesnrsquot warrant any additional return
Lecture 32
So What is Risk
bull Whether it is investing driving or just walking down the street everyone exposes themselves to risk
bull Risk is the chance that an investments actual return will be different than expected
bull This includes the possibility of losing some or all of the original investment
bull When investing in stocks bonds or any investment instrument there is a lot more risk than youd think
Letrsquos examine closer the different types of risk
Risk Types
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bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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39
Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
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19
bull Two general types
ndash Systematic Risk
ndash Non-systematic Risk
bull Systematic (general) Risk is a risk that influences a large number of assets
ndash An example is political events It is virtually impossible to protect yourself against this type of
risk
bull Pervasive affecting all securities cannot be avoided
bull Interest rate or market or inflation risks
bull Non-systematic (specific) Risk is Sometimes referred to as specific risk Its risk that affects a very
small number of assets
bull An example is news that affects a specific stock such as a sudden strike by employees
bull Total Risk = Systematic (General) Risk + Non-systematic (Specific) Risk
bull Diversification is the only way to protect yourself from unsystematic risk
Risk Sources
bull Interest Rate Risks
bull Market Risk
bull Inflation Risk
bull Business Risk
bull Financial Risk
bull Liquidity Risk
bull Exchange Rate Risk
bull Country Risk
bull Liquidity Risk
bull Marketability with-out sale prices
bull Financial Risk
bull Tied to debt financing
bull Inflation Risk
bull Purchasing power variability
bull Credit or Default Risk
bull This is the risk that a company or individual will be unable to pay the contractual interest or principal on
its debt obligations
bull This type of risk is of particular concern to investors who hold bonds within their portfolio
bull Government bonds especially those issued by the Federal government have the least amount of default
risk and least amount of returns while corporate bonds tend to have the highest amount of default risk
but also the higher interest rates
bull Country Risk
bull This refers to the risk that a country wont be able to honor its financial commitments When a country
defaults it can harm the performance of all other financial instruments in that country as well as other
countries it has relations with
bull Interest Rate Risk
bull A rise in interest rates during the term of your debt securities hurts the performance of stocks and bonds
bull Political Risk
bull This represents the financial risk that a countrys government will suddenly change its policies
bull This is a major reason that second and third world countries lack foreign investment
bull Market Risk - This is the most familiar of all risks
bull Its the day to day fluctuations in a stocks price
bull Also referred to as volatility
bull Market risk applies mainly to stocks and options As a whole stocks tend to perform well during a bull
market and poorly during a bear marketmdashvolatility is not so much a cause but an effect of certain
market forces
The Tradeoff Between
ER and Risk
bull Investors manage risk at a cost ndash means lower expected returns (ER)
bull Any level of expected return and risk can be attained
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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24
bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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20
The Return and Risk from Investing Asset Valuation
bull AV is a Function of both return and risk
ndash It is at the center of security analysis
bull How should realized return and risk be measured
bull The realized risk-return
bull The expected risk-return
ndash The realized risk-return tradeoff is based on the past
ndash The expected risk-return tradeoff is uncertain and may not occur
Return Components
bull Returns consist of two elements
ndash Periodic Cash Flows
ndash Price Appreciation or Depreciation
ndash Periodic cash flows such as interest or dividends (income return)
bull ―Yield measures relate income return to a price for the security
ndash Price appreciation or depreciation (capital gain or loss)
bull The change in price of the asset
bull Total Return =Yield + Price Change
Arithmetic Versus Geometric
bull Arithmetic mean does not measure the compound growth rate over time
ndash It does not capture the realized change in wealth over multiple periods
ndash But it does capture typical return in a single period
bull Geometric mean reflects compound cumulative returns over more than one period
Risk Premiums
bull Premium is additional return earned or expected for additional risk
ndash Calculated for any two asset classes
bull Equity Risk Premium
bull Bond Horizon Premium
bull Equity risk premium is the difference between stock and risk-free returns
bull Bond horizon premium is the difference between long- and short-term government securities
bull Equity Risk Premium (ERP) =
bull Bond Horizon Premium (BHP) =
The Risk-Return Record
bull Since 1920 cumulative wealth indexes show stock returns dominate bond returns
ndash Stock standard deviations also exceed bond standard deviations
bull Annual geometric mean return for the SampP 500 is 100 with standard deviation of 194
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return is a percentage relating all cash flows received during a given time period (denoted CFt
+(PE - PB) to the start of period price PB)
Risk
Risk-free Rate
Bonds
Stocks
RFCSTR
11
1
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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23
Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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TR= CFt + (PE - PB)
PB
Measuring Returns
bull We measure for comparing performance over time or across different securities
bull Total Return (TR) can be either positive or negative
ndash When cumulating or compounding negative returns are problem
bull A Return Relative (RR) solves the problem because it is always positive
RR= CFt + PE 1 + TR
PB
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull Cumulative Wealth Index CWIn over n periods =
bull To measure the level of wealth created by an investment rather than the change in wealth we need to
cumulate returns over time
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
ndash If foreign currency appreciates returns in local currency shall also grow
Measuring International Returns
bull International returns include any realized exchange rate changes
ndash If foreign currency depreciates returns are lower in domestic currency terms
bull Total Return in domestic currency =
Measures Describing a Return Series
bull TR (Total Return) RR (Return Relative) and CWI (Cumulative Wealth Index) are useful for a given
single time period
bull What about summarizing returns over several time periods
bull Arithmetic mean or simply mean
Geometric Mean
bull Defined as the n-th root of the product of n return relatives minus one or G =
bull Difference between Geometric mean and Arithmetic mean depends on the variability of returns
Adjusting Returns for Inflation
bull Returns measures are not adjusted for inflation
ndash Purchasing power of investment may change over time
ndash Consumer Price Index (CPI) is possible measure of inflation
Measuring Risk
bull Risk is the chance that the actual outcome is different than the expected outcome
bull Standard Deviation measures the deviation of returns from the mean
Lecture 33
Investment Decisions
bull Underlying investment decisions the tradeoff between expected return and risk
ndash Expected return is not usually the same as realized return
bull Risk the possibility that the realized return will be different than the expected return
bull The risk return tradeoff could easily be called the iron stomach test Deciding what amount of risk you
can take on while allowing you to get rest at night is an investorrsquos most important decision
The Investment Decision Process
bull Two-step process
) nTR)(TR)(TR( WI 121110
rr of ForCuBegin Val
f ForCurrEnd Val oRR 1
n
XX
Prepared by Humera Fazal Channab College
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Short Notes FIN 630 Chapters 23-45
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Short Notes FIN 630 Chapters 23-45
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
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ndash Security analysis and valuation
bull Necessary to understand security characteristics
ndash Portfolio management
bull Selected securities viewed as a single unit
bull How efficient are financial markets in processing new information
bull How and when should it be revised
bull How should portfolio performance be measured
Basic Strategies
ndash The basic decision involved in fixed-income management is the decision to be active or passive
ndash An active strategy has as its goal to secure superior returns from the fixed-income portfolio
ndash Superior returns can be earned if the investor can predict interest rate movements that are not
currently incorporated into price or if the investor can identify bonds that are mis-priced for other
factors
ndash For example finding a bond that has a credit risk premium that is too large for its credit risk
ndash Passive management involves controlling risk and balancing risk and return
Fixed Income
Passive Management
bull Bond-Index Funds
bull Immunization of interest rate risk
ndash Net worth immunization
Duration of assets = Duration of liabilities
ndash Target date immunization
Holding Period matches Duration
bull Cash flow matching and dedication
bull Bonds growth
Bond Index Fund
Contingent Immunization
bull Combination of active and passive management
bull Strategy involves active management with a floor rate of return
bull As long as the rate earned exceeds the floor the portfolio is actively managed
bull Once the floor rate or trigger rate is reached the portfolio is immunized
Factors Affecting the Process
bull Uncertainty in ex post returns dominates decision process
ndash Future unknown and must be estimated
bull Foreign financial assets opportunity to enhance return or reduce risk
bull Quick adjustments are needed to a changing environment
bull The Internet and the investment opportunities
bull Institutional investors are important
Portfolio theory Investment Decisions
bull Involve uncertainty
bull Focus on expected returns
ndash Estimates of future returns needed to consider and manage risk
bull Goal is to reduce risk without affecting returns
ndash Accomplished by building a portfolio
ndash Diversification is key
Dealing With Uncertainty
bull Risk that an expected return will not be realized
bull Investors must think about return distributions not just a single return
bull Probabilities weight outcomes
ndash Can be discrete or continuous
ndash Should be assigned to each possible outcome to create a distribution
ndash It helps to diversify
Calculating Expected Return
bull Expected value
ndash The single most likely outcome from a particular probability distribution
ndash The weighted average of all possible return outcomes
ndash Referred to as an ex ante or expected return
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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Short Notes FIN 630 Chapters 23-45
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25
bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Short Notes FIN 630 Chapters 23-45
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26
Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Short Notes FIN 630 Chapters 23-45
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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28
bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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Short Notes FIN 630 Chapters 23-45
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
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Calculation A Risk
bull Variance and standard deviation used to quantify and measure risk
ndash Measures the spread in the probability distribution
ndash Variance of returns σsup2 = (Ri - E(R))sup2pri
ndash Standard deviation of returns
σ =(σsup2)12
ndash Ex ante rather than ex post σ relevant
Portfolio Expected Return
bull Weighted average of the individual security expected returns
ndash Each portfolio asset has a weight w which represents the percent of the total portfolio value
Portfolio Expected Return
Asset Management
Portfolio Risk
bull Portfolio risk not simply the sum of individual security risks
bull Emphasis on the rate of risk of the entire portfolio and not on risk of individual securities in the
portfolio
bull Individual stocks are risky only if they add risk to the total portfolio
Example
bull Measured by the variance or standard deviation of the portfoliorsquos return
ndash Portfolio risk is not a weighted average of the risk of the individual securities in the portfolio
2
i
2
p
n
1i iw
Lecture 34
Risk Reduction in Portfolios
bull Assume all risk sources for a portfolio of securities are independent
bull The larger the number of securities the smaller the exposure to any particular risk
ndash ―Insurance principle
bull Only issue is how many securities to hold
bull Random diversification
ndash Diversifying without looking at relevant investment characteristics
ndash Marginal risk reduction gets smaller and smaller as more securities are added
bull A large number of securities is not required for significant risk reduction
bull International diversification benefits
Portfolio Risk and Diversification (see slide 19)
Markowitz Diversification
bull Non-random diversification
ndash Active measurement and management of portfolio risk
ndash Investigate relationships between portfolio securities before making a decision to invest
ndash Takes advantage of expected return and risk for individual securities and how security returns
move together
Measuring Portfolio Risk
bull Needed to calculate risk of a portfolio
ndash Weighted individual security risks
bull Calculated by a weighted variance using the proportion of funds in each security
bull For security i (wi times i)2
ndash Weighted co-movements between returns
bull Return co-variances are weighted using the proportion of funds in each security
bull For securities i j 2wiwj times ij
Correlation Coefficient
bull Statistical measure of association
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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30
bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
Prepared by Humera Fazal Channab College
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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Short Notes FIN 630 Chapters 23-45
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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bull mn = correlation coefficient between securities m and n
ndash mn = +10 = perfect positive correlation
ndash mn = -10 = perfect negative (inverse) correlation
ndash mn = 00 = zero correlation
bull When does diversification pay
ndash With perfectly positive correlated securities
bull Risk is a weighted average therefore there is no risk reduction
ndash With zero correlation correlation securities
ndash With perfectly negative correlated securities
Covariance
bull Absolute measure of association
ndash Not limited to values between -1 and +1
ndash Sign interpreted the same as correlation
ndash Correlation coefficient and covariance are related by the following equations
Calculating Portfolio Risk
bull Encompasses three factors
ndash Variance (risk) of each security
ndash Covariance between each pair of securities
ndash Portfolio weights for each security
bull Goal select weights to determine the minimum variance combination for a given level of expected
return
bull Generalizations
ndash The smaller the positive correlation between securities the better
ndash Covariance calculations grow quickly
bull n(n-1) for n securities
ndash As the number of securities increases
bull The importance of covariance relationships increases
bull The importance of each individual securityrsquos risk decreases
Simplifying Markowitz Calculations
bull Markowitz full-covariance model
ndash Requires a covariance between the returns of all securities in order to calculate portfolio
variance
ndash n(n-1)2 set of co-variances for n securities
bull Markowitz suggests using an index to which all securities are related to simplify
An Efficient Portfolio
bull Smallest portfolio risk for a given level of expected return
bull Largest expected return for a given level of portfolio risk
bull From the set of all possible portfolios
ndash Only locate and analyze the subset known as the efficient set
bull Lowest risk for given level of return
bull All other portfolios in attainable set are dominated by efficient set
bull Global minimum variance portfolio
ndash Smallest risk of the efficient set of portfolios
bull Efficient set
ndash Part of the efficient frontier with greater risk than the global minimum variance portfolio
Lecture 35
Portfolio Selection
bull Diversification is key to optimal risk management
bull Analysis required because of the infinite number of portfolios of risky assets
bull How should investors select the best risky portfolio
bull How could riskless assets be used
Building a Portfolio
bull Step 1
bull Use the Markowitz portfolio selection model to identify optimal combinations
ndash Estimate expected returns risk and each covariance between returns
bull Step 2
Prepared by Humera Fazal Channab College
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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34
ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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bull Choose the final portfolio based on your preferences for return relative to risk
Portfolio Theory
bull Optimal diversification takes into account all available information
bull Assumptions in portfolio theory
ndash A single investment period (one year)
ndash Liquid position (no transaction costs)
ndash Preferences based only on a portfoliorsquos expected return and risk
Efficient Portfolios
bull Efficient frontier or Efficient set (curved line from A to B)
bull Global minimum variance portfolio (represented by point A)
Selecting an Optimal Portfolio of Risky Assets
bull Assume investors are risk averse
bull Indifference curves help select from efficient set
ndash Description of preferences for risk and return
ndash Portfolio combinations which are equally desirable
ndash Greater slope implies greater the risk aversion
bull Markowitz portfolio selection model
ndash Generates a frontier of efficient portfolios which are equally good
ndash Does not address the issue of riskless borrowing or lending
ndash Different investors will estimate the efficient frontier differently
bull Element of uncertainty in application
The Single Index Model (slide 20)
bull Relates returns on each security to the returns on a common index such as the SampP 500 Stock Index
bull Expressed by the following equation
bull Divides return into two components
ndash a unique part ai
ndash a market-related part biRM
ndash b measures the sensitivity of a stock to stock market movements
ndash If securities are only related in their common response to the market
bull Securities covary together only because of their common relationship to the market
index
bull Security covariance depend only on market risk and can be written as
bull Single index model helps split a securityrsquos total risk into
ndash Total risk = market risk + unique risk (slid 22)
bull Multi-Index models as an alternative
ndash Between the full variance-covariance method of Markowitz and the single-index model
Selecting Optimal Asset Classes
bull Another way to use Markowitz model is with asset classes
ndash Allocation of portfolio assets to broad asset categories
bull Asset class rather than individual security decisions most important for investors
ndash Different asset classes offers various returns and levels of risk
bull Correlation coefficients may be quite low
x
B
A
C y
Risk =
E(R)
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Asset Allocation
bull Decision about the proportion of portfolio assets allocated to equity fixed-income and money market
securities
ndash Widely used application of Modern Portfolio Theory
ndash Because securities within asset classes tend to move together asset allocation is an important
investment decision
ndash Should consider international securities real estate and US Treasury TIPS
Balanced Portfolio
Implications of Portfolio Selection
bull Investors should focus on risk that cannot be managed by diversification
bull Total risk =systematic (non-diversifiable) risk + nonsystematic (diversifiable) risk
ndash Systematic risk
bull Variability in a securityrsquos total returns directly associated with economy-wide events
bull Common to virtually all securities
ndash Both risk components can vary over time
bull Affects number of securities needed to diversify
Lecture 36
Asset Pricing Models
Capital Asset Pricing Model
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
CAPM Assumptions
bull CAPM focuses on the equilibrium relationship between the risk and expected return on risky assets
bull It builds on Markowitz portfolio theory
bull Each investor is assumed to diversify his or her portfolio according to the Markowitz model
bull No transaction costs no personal income taxes no inflation
bull No single investor can affect the price of a stock
bull Capital markets are in equilibrium
Borrowing and Lending Possibilities
bull Risk free assets
ndash Certain-to-be-earned expected return and a variance of return of zero
ndash No correlation with risky assets
ndash Usually proxied by a Treasury security
bull Amount to be received at maturity is free of default risk known with certainty
bull Adding a risk-free asset extends and changes the efficient frontier
Risk-Free Lending
bull Riskless assets can be combined with any portfolio in the efficient set AB
ndash Z implies lending
bull Set of portfolios on line RF to T dominates all portfolios below it
Number of securities in portfolio 10 20 30 40 100+
Portfolio risk
Market Risk
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
Prepared by Humera Fazal Channab College
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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30
bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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31
ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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32
ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
Prepared by Humera Fazal Channab College
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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Impact of Risk-Free Lending
bull If wRF placed in a risk-free asset
ndash Expected portfolio return
ndash Risk of the portfolio
bull Expected return and risk of the portfolio with lending is a weighted average
Borrowing Possibilities
bull Investor no longer restricted to own wealth
bull Interest paid on borrowed money
ndash Higher returns sought to cover expense
ndash Assume borrowing at RF
bull Risk will increase as the amount of borrowing increases
ndash Financial leverage
The New Efficient Set
bull Risk-free investing and borrowing creates a new set of expected return-risk possibilities
bull Addition of risk-free asset results in
ndash A change in the efficient set from an arc to a straight line tangent to the feasible set without the
riskless asset
ndash Chosen portfolio depends on investorrsquos risk-return preferences
Portfolio Choice
bull The more conservative the investor the more is placed in risk-free lending and the less borrowing
bull The more aggressive the investor the less is placed in risk-free lending and the more borrowing
ndash Most aggressive investors would use leverage to invest more in portfolio T
Market Portfolio
bull Most important implication of the CAPM
ndash All investors hold the same optimal portfolio of risky assets
ndash The optimal portfolio is at the highest point of tangency between RF and the efficient frontier
ndash The portfolio of all risky assets is the optimal risky portfolio
bull Called the market portfolio
Characteristics of the Market Portfolio
bull All risky assets must be in portfolio so it is completely diversified
ndash Includes only systematic risk
bull All securities included in proportion to their market value
bull Unobservable but proxied by SampP 500
bull Unobservable but proxied by KSE 100 index
bull Contains worldwide assets
ndash Financial and real assets
Capital Market Line
bull Line from RF to L is capital market line (CML)
Risk
B
A
T E(R)
RF
L
Z X
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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Short Notes FIN 630 Chapters 23-45
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
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bull x = risk premium =E(RM) - RF
bull y =risk =M
bull Slope =xy
=[E(RM) - RF]M
bull y-intercept = RF
The Separation Theorem
bull Investors use their preferences (reflected in an indifference curve) to determine their optimal portfolio
bull Separation Theorem
ndash The investment decision which risky portfolio to hold is separate from the financing decision
ndash Allocation between risk-free asset and risky portfolio separate from choice of risky portfolio T
bull All investors
ndash Invest in the same portfolio
ndash Attain any point on the straight line RF-T-L by by either borrowing or lending at the rate RF
depending on their preferences
bull Risky portfolios are not tailored to each individualrsquos taste
Capital Market Line
bull Slope of the CML is the market price of risk for efficient portfolios or the equilibrium price of risk in
the market
bull Relationship between risk and expected return for portfolio P (Equation for CML) slide 29 formula
Security Market Line
bull CML Equation only applies to markets in equilibrium and efficient portfolios
bull The Security Market Line depicts the tradeoff between risk and expected return for individual securities
bull Under CAPM all investors hold the market portfolio
ndash How does an individual security contribute to the risk of the market portfolio
bull A securityrsquos contribution to the risk of the market portfolio is based on beta
bull Equation for expected return for an individual stock slid 31
bull Beta = 10 implies as risky as market
bull Securities A and B are more risky than the market
ndash Beta gt10
bull Security C is less risky than the market
ndash Beta lt10 (slid 32)
bull Beta measures systematic risk
ndash Measures relative risk compared to the market portfolio of all stocks
ndash Volatility different than market
bull All securities should lie on the SML
ndash The expected return on the security should be only that return needed to compensate for
systematic risk
Lecture 37
CAPMrsquos Expected Return-Beta Relationship
bull Required rate of return on an asset (ki) is composed of
ndash Risk-free rate (RF)
ndash Risk premium (i [ E(RM) - RF ])
bull Market risk premium adjusted for specific security
E(RM
)
RF
Risk
M
L
M
y
x
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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31
ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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32
ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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Short Notes FIN 630 Chapters 23-45
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33
VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ki = RF +i [ E(RM) - RF ]
ndash The greater the systematic risk the greater the required return
Estimating the SML
bull Treasury Bill rate used to estimate RF
bull Expected market return unobservable
ndash Estimated using past market returns and taking an expected value
bull Estimating individual security betas difficult
ndash Only company-specific factor in CAPM
ndash Requires asset-specific forecast
Capital Market Line
Estimating Beta
bull Market model
bull Characteristic line
Estimating Beta
bull Market model
ndash Relates the return on each stock to the return on the market assuming a linear relationship
Ri =i +i RM +ei
bull Characteristic line
ndash Line fit to total returns for a security relative to total returns for the market index
Betas
How Accurate Are Beta Estimates
bull Betas change with a companyrsquos situation
ndash Not stationary over time
bull Estimating a future beta
ndash May differ from the historical beta
bull RM represents the total of all marketable assets in the economy
ndash Approximated with a stock market index
ndash Approximates return on all common stocks
bull No one correct number of observations and time periods for calculating beta
bull The regression calculations of the true and from the characteristic line are subject to error in
estimation
bull Portfolio betas more reliable than individual security betas
Assessments
Arbitrage Pricing Theory
bull Based on the Law of One Price
ndash Two otherwise identical assets cannot sell at different prices
ndash Equilibrium prices adjust to eliminate all arbitrage opportunities
bull Unlike CAPM APT does not assume
ndash Single-period investment horizon absence of personal taxes riskless borrowing or lending
mean-variance decisions
Factors
bull APT assumes returns generated by a factor model
bull Factor Characteristics
ndash Each risk must have a pervasive influence on stock returns
ndash Risk factors must influence expected return and have non-zero prices
ndash Risk factors must be unpredictable to the market
APT Model
bull Most important are the deviations of the factors from their expected values
bull The expected return-risk relationship for the APT can be described as
E(Ri) =RF +bi1 (risk premium for factor 1) +bi2 (risk premium for factor 2) +hellip +bin (risk premium for
factor n)
Problems with APT
bull Factors are not well specified
ndash To implement the APT model need the factors that account for the differences among security
returns
bull CAPM identifies market portfolio as single factor
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Short Notes FIN 630 Chapters 23-45
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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Short Notes FIN 630 Chapters 23-45
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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Short Notes FIN 630 Chapters 23-45
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
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40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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bull Neither CAPM or APT has been proven superior
ndash Both rely on unobservable expectations
Arbitrage Pricing Theory
Portfolio Management
bull Involves decisions that must be made by every investor whether an active or passive investment
approach is followed
bull Relationships between various investment alternatives must be considered if an investor is to hold an
optimal portfolio
Portfolio Management as a Process
bull Definite structure everyone can follow
bull Integrates a set of activities in a logical and orderly manner
bull Continuous and systematic
bull Encompasses all portfolio investments
bull With a structured process anyone can execute decisions for investor
bull Objectives constraints and preferences are identified
bull Leads to explicit investment policies
bull Strategies developed and implemented
bull Market conditions asset mix and investor circumstances are monitored
bull Portfolio adjustments are made as necessary
Individual vs Institutional Investors
Institutional Investors Individual Investors
Maintain relatively constant profile
over time
Life stage matters
Legal and regulatory constraints Risk defined as ―losing
money
Well-defined and effective policy is
critical
Characterized by
personalities
Individual Investors
ndash Goals are important
ndash Tax management is important part of decisions
Institutional Investors
bull Primary reason for establishing a long-term investment policy for institutional investors
ndash Prevents arbitrary revisions of a soundly designed investment policy
ndash Helps portfolio manager to plan and execute on a long-term basis
bull Short-term pressures resisted
Lecture 38
Life Cycle Approach
bull Riskreturn position at various life cycle stages
A Accumulation phase - early career
B Consolidation phase - mid-to late career
C Spending phase - spending and gifting
Formulate Investment Policy
bull Investment policy summarizes the objectives constraints and preferences for the investor
bull Information needed
ndash Objectives
bull Return requirements and risk tolerance
Risk
Return
C
B
A
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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Short Notes FIN 630 Chapters 23-45
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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ndash Constraints and Preferences
bull Liquidity time horizon laws and regulations taxes unique preferences circumstances
bull Investment policy should contain a statement about inflation adjusted returns
ndash Clearly a problem for investors
ndash Common stocks are not always an inflation hedge
bull Unique needs and circumstances
ndash May restrict certain asset classes
bull Risky Assets
bull Riskless Assets
bull Preferences
bull No of assets portfolios based on personal constraints or preferences
bull Constraints and Preferences
ndash Time horizon
bull Objectives may require specific planning horizon
ndash Liquidity needs
bull Investors should know future cash needs
ndash Tax considerations
bull Ordinary income vs capital gains
bull Retirement programs offer tax sheltering
Legal and Regulatory Requirements
bull Prudent Man Rule
ndash Followed in fiduciary responsibility
ndash Interpretation can change with time and circumstances
ndash Standard applied to individual investments rather than the portfolio as a whole
bull Diversification and standards applied to entire portfolio
Portfolio
Capital Market Expectations
bull Macro factors
ndash Expectations about the capital markets
bull Micro factors
ndash Estimates that influence the selection of a particular asset for a particular portfolio
bull Rate of return assumptions
ndash Make them realistic
ndash Study historical returns carefully
ndash Qualitative amp quantitative data based on historical data
Rate of Return Assumptions
bull How much influence should recent stock market returns have
ndash Mean reversion arguments
ndash Stock returns involve considerable risk
bull Probability of 10 return is 50 regardless of the holding period
bull Probability of gt10 return decreases over longer investment horizons
ndash Expected returns are not guaranteed
Constructing the Portfolio
bull Use investment policy and capital market expectations to choose portfolio of assets
ndash Define securities eligible for inclusion in a particular portfolio
ndash Use an optimization procedure to select securities and determine the proper portfolio weights
bull Markowitz provides a formal model
bull Numbers game
bull Capital gains
bull Returns
bull Required rate of return
bull Time horizon
Asset Allocation
bull Involves deciding on weights for cash bonds and stocks
ndash Most important decision
bull Differences in allocation cause differences in portfolio performance
bull Factors to consider
Prepared by Humera Fazal Channab College
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
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34
ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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35
ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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ndash Return requirements risk tolerance time horizon age of investor
bull Strategic asset allocation
ndash Simulation procedures used to determine likely range of outcomes associated with each asset
mix
bull Establishes long-run strategic asset mix
bull Tactical asset allocation
ndash Changes is asset mix driven by changes in expected returns
ndash Market timing approach
Monitoring Conditions and Circumstances
bull Investor circumstances can change for several reasons
ndash Wealth changes affect risk tolerance
ndash Investment horizon changes
ndash Liquidity requirement changes
ndash Tax circumstance changes
ndash Regulatory considerations
ndash Unique needs and circumstances
Portfolio Adjustments
bull Portfolio not intended to stay fixed
bull Key is to know when to rebalance
bull Rebalancing cost involves
ndash Brokerage commissions
ndash Possible impact of trade on market price
ndash Time involved in deciding to trade
bull Cost of not rebalancing involves holding unfavorable positions
Performance Measurement
bull Allows measurement of the success of portfolio management
bull Key part of monitoring strategy and evaluating risks
bull Important for
ndash Those who employ a manager
ndash Those who invest personal funds
bull Find reasons for success or failure
Evaluation of the Investment Process
How Should Portfolio Performance Be Evaluated
bull Bottom line issue in investing
bull Is the return after all expenses adequate compensation for the risk
bull What changes should be made if the compensation is too small
bull Performance must be evaluated before answering these questions
Lecture 39
Considerations
bull Without knowledge of risks taken little can be said about performance
ndash Intelligent decisions require an evaluation of risk and return
ndash Risk-adjusted performance best
bull Relative performance comparisons
ndash Benchmark portfolio must be legitimate alternative that reflects objectives
bull Evaluation of portfolio manager or the portfolio itself
ndash Portfolio objectives and investment policies matter
bull Constraints on managerial behavior affect performance
bull How well-diversified during the evaluation period
ndash Adequate return for diversifiable risk
bull Age of investors
bull Financial liquidity strength of the investors
bull The cash flow requirement of the investors
bull The risk tolerance of the investors
Return Measures
bull Change in investorrsquos total wealth over an evaluation period
(VE - VB) VB
VE =ending portfolio value
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
Prepared by Humera Fazal Channab College
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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VB =beginning portfolio value
bull Assumes no funds added or withdrawn during evaluation period
ndash If not timing of flows important
Return Measures
bull Portfolios is the mean of enhancing the somebodys capital gains capital wealth and his financial status
as well
bull Dollar-weighted returns
bull Time-weighted returns
bull Dollar-weighted returns
ndash Captures cash flows during the evaluation period
ndash Equivalent to internal rate of return
ndash Equates initial value of portfolio (investment) with cash inflows or outflows and ending value of
portfolio
(VE - VB) VB ndash Cash flow effects make comparisons to benchmarks inappropriate
ndash Time-weighted returns
ndash Captures cash flows during the evaluation period and permits comparisons with benchmarks
ndash Calculate a return relative for each time period defined by a cash inflow or outflow
ndash Use each return relative to calculate a compound rate of return for the entire period
Which Return Measure Should Be Used
bull Dollar- and Time-weighted Returns can give different results
ndash Dollar-weighted returns appropriate for portfolio owners
ndash Time-weighted returns appropriate for portfolio managers
bull No control over inflows outflows
bull Independent of actions of client
bull One could look at time-weighted returns results
Risk Measures
bull Risk differences cause portfolios to respond differently to market changes
bull Total risk measured by the standard deviation of portfolio returns
bull Non-diversifiable risk measured by a securityrsquos beta
ndash Estimates may vary be unstable and change over time
Risk-Adjusted Performance
bull The Sharpe reward-to-variability ratio
ndash Benchmark based on the ex post capital market line
=Average excess return total risk
ndash Risk premium per unit of risk
ndash The higher the better the performance
ndash Provides a ranking measure for portfolios
bull The Treynor reward-to-volatility ratio
ndash Distinguishes between total and systematic risk
ndash =Average excess return market risk
ndash Risk premium per unit of market risk
ndash The higher the better the performance
ndash Implies a diversified portfolio
RVAR or RVOL
bull Depends on the definition of risk
ndash If total risk best use RVAR
ndash If systematic risk best use RVOL
ndash If portfolios perfectly diversified rankings based on either RVAR or RVOL are the same
ndash Differences in diversification cause ranking differences
bull RVAR captures portfolio diversification
Measuring Diversification
bull How correlated are portfoliorsquos returns to market portfolio
ndash R2 from estimation of
Rpt - RFt =ap +bp [RMt - RFt] +ept
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash R2 is the coefficient of determination
ndash Excess return form of characteristic line
ndash The lower the R2 the greater the diversifiable risk and the less diversified
Jensenrsquos Alpha
bull The estimated a coefficient in
Rpt - RFt =ap +bp [RMt - RFt] +ept
is a means to identify superior or inferior portfolio performance
ndash CAPM implies a is zero
ndash Measures contribution of portfolio manager beyond return attributable to risk
bull If a gt0 (lt0=0) performance superior (inferior equals) to market risk-adjusted
Measurement Problems
bull Performance measures based on CAPM and its assumptions
ndash Riskless borrowing
ndash What should market proxy be
bull If not efficient benchmark error
bull Global investing increases problem
bull How long an evaluation period
ndash One could look at a 10 year period
Other Evaluation Issues
bull Performance attribution seeks an explanation for success or failure
ndash Analysis of investment policy and asset allocation decision
ndash Analysis of industry and security selection
ndash Benchmark (bogey) selected to measure passive investment results
ndash Differences due to asset allocation market timing security selection
There are three broad categories of securities
Three Reasons for Investing
People invest to hellip
bull Earn capital gains
ndash Appreciation refers to an increase in the value of an investment
bull Supplement their income
ndash Dividends and Interest
bull Experience the excitement of the investment process
Lecture 40
What are Derivatives
bull Derivatives are instruments whose values depend on the value of other more basic underlying variables
Their value derives from some other asset
ndash A derivative is a financial instrument whose return is derived from the return on another
instrument
The underlying assets could be
Financial Assets
Commodities
Real Assets
The Rationale for Derivative Assets
The first organized derivatives exchange (in the United States) was developed in order to bring stability
to agricultural prices by enabling farmers to eliminate or reduce their price risk
Introduction
bull There is no universally satisfactory answer to the question of ―What a derivative is
bull Often when a market participant suffers a large newsworthy loss the term ―derivatives is used almost
as of it were an explanation
ndash ―anything that results in a large loss
Securities
Equity Securities eg common
stock
Derivative Assets eg futures
options
Fixed Income Securities eg bonds
preferred stock
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
Prepared by Humera Fazal Channab College
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
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Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
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(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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ndash ―dreaded D word
ndash ―beef derivative
bull Futures and options markets are very useful perhaps even essential parts of the financial system
bull Futures and options markets have a long history of being misunderstood
Derivatives Markets
bull Exchange traded
ndash Contracts are standard there is virtually no credit risk
ndash Traditionally exchanges have used the open-outcry system but increasingly they are switching to
electronic trading
bull Over-the-counter (OTC)
ndash A computer- and telephone-linked network of dealers at financial institutions corporations and
fund managers
ndash Contracts can be non-standard and there is some small amount of credit risk
Role of Derivative Assets
bull Derivative assets
ndash The best-known derivative assets are futures and options contracts
ndash Derivatives are not all the same Some are inherently speculative while some are highly
conservative
Derivatives Instruments
bull Futures Contracts
bull Forwards Contracts
bull Options
bull Swaps
Futures Contract
bull Traded on exchanges
bull It is an agreement to sell or buy in future like a forward contract
Forward Contract
bull Traded in Over-the-Counter Market
bull It is an agreement to buy or sell an asset at a certain future time for a certain price
bull Option contract gives the owner of the contract a right but not an obligation to buysell in the future
bull Traded both at exchanges and over-the-counter markets
bull Swap
bull It is an agreement to exchange cash flows at specified future times according to certain specified rules
Types of Derivatives
bull Options
bull Futures contracts
bull Swaps
bull Product Characteristics
Options
bull An option is the right to either buy or sell something at a set price within a set period of time
ndash The right to buy is a call option
ndash The right to sell is a put option
bull You can exercise an option if you wish but you do not have to do so
Futures Contracts
bull Futures contracts involve a promise to exchange a product for cash by a set delivery date
bull Futures contracts deal with transactions that will be made in the future
bull Are different from options in that
bull The buyer of an option can abandon the option if he or she wishes
bull The buyer of a futures contract cannot abandon the contract
Futures Contracts Example
bull The futures market deals with transactions that will be made in the future A person who buys a
December US Treasury bond futures contract promises to pay a certain price for treasury bonds in
December If you buy the T-bonds today you purchase them in the cash or spot market
Futures Contracts
bull A futures contract involves a process known as marking to market
ndash Money actually moves between accounts each day as prices move up and down
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bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
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Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
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ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
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Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
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bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
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bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
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Short Notes FIN 630 Chapters 23-45
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36
bull A forward contract is functionally similar to a futures contract however
ndash There is no marking to market
ndash Forward contracts are not marketable
SWAPS
bull Swaps are arrangements in which one party trades something with another party
bull The swap market is very large with trillions of dollars outstanding
Interest Rate Swap
In an interest rate swap one firm pays a fixed interest rate on a sum of money and receives from some other
firm a floating interest rate on the same sum
Foreign Currency Swap
bull In a foreign currency swap two firms initially trade one currency for another
bull Subsequently the two firms exchange interest payments one based on a foreign interest rate and the other
based on a US interest rate
bull Finally the two firms re-exchange the two currencies
Product Characteristics
bull Both options and futures contracts exist on a wide variety of assets
ndash Options trade on individual stocks on market indexes on metals interest rates or on futures contracts
ndash Futures contracts trade on products such as wheat live cattle gold heating oil foreign currency US
Treasury bonds and stock market indexes
bull The underlying asset is that which you have the right to buy or sell (with options) or to buy or deliver (with
futures)
bull Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange (CBOE) or
the Chicago Board of Trade (CBT)
bull OTC derivatives are customized products that trade off the exchange and are individually negotiated
between two parties
bull Options are securities and are regulated by the Securities and Exchange Commission (SEC)
bull Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)
Lecture 41
Key Points About Futures
bull They are settled daily
bull Closing out a futures position involves entering into an offsetting trade
bull Most contracts are closed out before maturity
Features of Future Contracts
bull Available on a wide range of underlying assets
bull Exchange traded
bull Specifications need to be defined
ndash The Underlying This can be anything from a barrel of sweet crude oil to a short term interest
rate
ndash The Amount And Units Of The Underlying Asset Per Contract
ndash The Delivery Month
ndash The Last Trading Date
ndash The Grade Of The Deliverable
ndash The Type Of Settlement either cash settlement or physical settlement
ndash The Currency in which the futures contract is quoted
bull Settled daily for profits losses
Delivery
bull If a futures contract is not closed out before maturity it is usually settled by delivering the assets
underlying the contract
bull When there are alternatives about what is delivered where it is delivered and when it is delivered the
party with the short position chooses
Margins
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Understanding Futures Markets
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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39
Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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37
bull Spot or cash market
ndash Price refers to item available for immediate delivery
bull Forward market
ndash Price refers to item available for delayed delivery
bull Futures market
ndash Sets features (contract size delivery date and conditions) for delivery
bull Futures market characteristics
ndash Centralized marketplace allows investors to trade each other
ndash Performance is guaranteed by a clearinghouse
bull Valuable economic functions
ndash Hedgers shift price risk to speculators
ndash Price discovery conveys information
bull Commodities - agricultural metals and energy related
bull Financials - foreign currencies as well as debt and equity instruments
bull Foreign futures markets
ndash Increased number shows the move toward globalization
bull Markets quite competitive with US environment
Futures Contract
bull A obligation to buy or sell a fixed amount of an asset on a specified future date at a price set today
ndash Trading means that a commitment has been made between buyer and seller
ndash Position offset by making an opposite contract in the same commodity
bull Commodity Futures Trading Commission regulates trading
Futures Exchanges
bull Where futures contracts are traded
bull Voluntary nonprofit associations of membership
bull Organized marketplace where established rules govern conduct
ndash Funded by dues and fees for services rendered
bull Members trade for self or for others
The Clearinghouse
bull A corporation separate from but associated with each exchange
bull Exchange members must be members or pay a member for these services
ndash Buyers and sellers settle with clearinghouse not with each other
bull Helps facilitate an orderly market
bull Keeps track of obligations
The Mechanics of Trading
bull Through open-outcry seller and buyer agree to take or make delivery on a future date at a price agreed
on today
ndash Short position (seller) commits a trader to deliver an item at contract maturity
ndash Long position (buyer) commits a trader to purchase an item at contract maturity
ndash Like options futures trading a zero sum game
bull How contracts are settled
bull Contracts can be settled in two ways
ndash Delivery (less than 2 of transactions)
ndash Offset liquidation of a prior position by an offsetting transaction
bull Each exchange establishes price fluctuation limits on contracts
bull No restrictions on short selling
Margin
bull A margin is cash or marketable securities deposited by an investor with his or her broker
bull The balance in the margin account is adjusted to reflect daily settlement
bull Margins minimize the possibility of a loss through a default on a contract
Futures (Margin)
Earnest money deposit made by both buyer and seller to ensure performance of obligations
ndash Not an amount borrowed from broker
bull Each clearinghouse sets requirements
ndash Brokerage houses can require higher margin
bull Initial margin usually less than 10 of contract value
Futures (Margin calls)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
39
Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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httpgroupsgooglecomgroupvuzs
42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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httpgroupsgooglecomgroupvuzs
44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
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Short Notes FIN 630 Chapters 23-45
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45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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38
bull Margin calls occur when price goes against investor
ndash Must deposit more cash or close account
ndash Position marked-to-market daily
ndash Profit can be withdrawn
Lecture 42
Participants in the Derivatives World
bull Hedging
bull Speculation
bull Arbitrage
Ways Derivatives are Used
bull To hedge risks
bull To speculate (take a view on the future direction of the market)
bull To lock in an arbitrage profit
bull To change the nature of a liability
bull To change the nature of an investment without incurring the costs of selling one portfolio and buying
another
First Type of Trader
bull Hedger A person who uses derivatives to reduce risk that they may face in future
Using Future Contracts Hedging
bull If someone bears an economic risk and uses the futures market to reduce that risk the person is a
hedger
bull Hedging is a prudent business practice and a prudent manager has a legal duty to understand and use the
futures market hedging mechanism
Using Futures Contracts
bull Hedgers
ndash At risk with a spot market asset and exposed to unexpected price changes
ndash Buy or sell futures to offset the risk
ndash Used as a form of insurance
ndash Willing to forgo some profit in order to reduce risk
bull Hedged return has smaller chance of low return but also smaller chance of high
Hedging
bull Short (sell) hedge
ndash Cash market inventory exposed to a fall in value
ndash Sell futures now to profit if the value of the inventory falls
bull Long (buy) hedge
ndash Anticipated purchase exposed to a rise in cost
ndash Buy futures now to profit if costs increase
Hedging Examples
bull A US company will pay pound10 million for imports from Britain in 3 months and decides to hedge using a
long position in a forward contract
bull An investor owns 1000 Microsoft shares currently worth $28 per share A two-month put with a strike
price of $2750 costs $1 The investor decides to hedge by buying 10 contracts
Value of Microsoft Shares with and without Hedging
Second Type of Trader
bull Speculator A person who uses derivatives to bet on the future direction of the market
Speculation
bull A person or firm who accepts the risk the hedger does not want to take is a speculator
bull Speculators believe the potential return outweighs the risk
bull The primary purpose of derivatives markets is not speculation Rather they permit the transfer of risk
between market participants as they desire
20000
25000
30000
35000
40000
20 25 30 35 40
Stock Price ($)
Value of
Holding ($)
No Hedging
Hedging
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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39
Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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httpgroupsgooglecomgroupvuzs
41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
39
Speculation Example
bull An investor with $4000 to invest feels that amazoncomrsquos stock price will increase over the next 2
months The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2
Third Type of Trader
bull Arbitrageur A person who takes two opposite positions on the same instrument in two different
markets to earn a profit
bull Derivatives are excessively used for all these purposes
Arbitrage
bull Arbitrage is the existence of a riskless profit
bull Arbitrage opportunities are quickly exploited and eliminated
bull Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs
bull Arbitrageurs keep prices in the marketplace efficient
bull An efficient market is one in which securities are priced in accordance with their perceived level
of risk and their potential return
Arbitrage Example
bull A stock price is quoted as pound100 in London and $172 in New York
bull The current exchange rate is 17500
Hedging Risks
bull Basis difference between cash price and futures price of hedged item
ndash Must be zero at contract maturity
bull Basis risk the risk of an unexpected change in basis
ndash Hedging reduces risk if basis risk less than variability in price of hedged asset
bull Risk cannot be entirely eliminated
Hedging with Stock Index Futures
bull Selling futures contracts against diversified stock portfolio allows the transfer of systematic risk
ndash Diversification eliminates nonsystematic risk
ndash Hedging against overall market decline
ndash Offset value of stock portfolio because futures prices are highly correlated with changes in value
of stock portfolios
Using Futures Contracts
bull Speculators
ndash Buy or sell futures contracts in an attempt to earn a return
bull No prior spot market position
ndash Absorb excess demand or supply generated by hedgers
ndash Assuming the risk of price fluctuations that hedgers wish to avoid
ndash Speculation encouraged by leverage ease of transacting low costs
Speculating with Stock Index Futures
bull Futures effective for speculating on movements in stock market because
ndash Low transaction costs involved in establishing futures position
ndash Stock index futures prices mirror the market
bull Traders expecting the market to rise (fall) buy (sell) index futures
bull Futures contract spreads
ndash Both long and short positions at the same time in different contracts
ndash Intramarket (or calendar or time) spread
bull Same contract different maturities
ndash Intermarket (or quality) spread
bull Same maturities different contracts
bull Interested in relative price as opposed to absolute price changes
Financial Futures
bull Contracts on equity indexes fixed income securities and currencies
bull Opportunity to fine-tune risk-return characteristics of portfolio
bull At maturity stock index futures settle in cash
ndash Difficult to manage delivery of all stocks in a particular index
bull At maturity Treasury bond and Treasury bill interest rate futures settle by delivery of debt instruments
ndash If expect increase in rates sell interest rate futures
ndash If expect decrease in rates buy interest rate futures
bull Increase (decrease) in interest rates will decrease (increase) spot and futures prices
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
40
ndash Difficult to short bonds in spot market
Program Trading
bull Index arbitrage a version of program trading
ndash Exploitation of price difference between stock index futures and index of stocks underlying
futures contract
ndash Arbitrageurs build hedged portfolio that earns low risk profits equaling the difference between
the value of cash and futures positions
Lecture 43
Example of a Futures Trade
An investor takes a long position in two December gold futures contracts on June 5
ndash Contract size is 100 oz
ndash Futures price is US$400
ndash Margin requirement is US$2000contract (US$4000 in total)
ndash Maintenance margin is US$1500contract (US$3000 in total)
A Possible Outcome
Long amp Short Hedges
bull A long futures hedge is appropriate when you know you will purchase an asset in the future and want
to lock in the price
bull A short futures hedge is appropriate when you know you will sell an asset in the future amp want to lock
in the price
Basis Risk
bull Basis is the difference between spot amp futures
bull Business risk arises because of the uncertainty about the basis when the hedge is closed out
Long Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future purchase of an asset by entering into a long futures contract
bull Cost of Asset=S2 ndash (F2 ndash F1) = F1 + Basis
Short Hedge
bull Suppose that
F1 Initial Futures Price
F2 Final Futures Price
S2 Final Asset Price
bull You hedge the future sale of an asset by entering into a short futures contract
bull Price Realized=S2+ (F1 ndash F2) = F1 + Basis
Choice of Contract
bull Choose a delivery month that is as close as possible to but later than the end of the life of the hedge
bull When there is no futures contract on the asset being hedged choose the contract whose futures price is
most highly correlated with the asset price This is known as cross hedging
Reasons for Hedging an Equity Portfolio
bull Desire to be out of the market for a short period of time
bull Hedging may be cheaper than selling the portfolio and buying it back
bull Desire to hedge systematic risk
bull Appropriate when you feel that you have picked stocks that will outperform the market
Daily Cumulative Margin
Futures Gain Gain Account Margin
Price (Loss) (Loss) Balance Call
Day (US$) (US$) (US$) (US$) (US$)
40000 4000
5-Jun 39700 (600) (600) 3400 0
13-Jun 39330 (740) (1340) 2660 1340
19-Jun 38700 (1260) (2600) 2740 1260
26-Jun 39230 1060 (1540) 5060 0
+
= 4000
3000
+
= 4000
lt
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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41
Hedging Price of an Individual Stock
bull Similar to hedging a portfolio
bull Does not work as well because only the systematic risk is hedged
bull The unsystematic risk that is unique to the stock is not hedged
Hedge Equity Returns
bull May want to be out of the market for a while
bull Hedging avoids the costs of selling and repurchasing the portfolio
bull Suppose stocks in your portfolio have an above average EPS but you feel they have been chosen well
and will outperform the market in both good and bad times Hedging ensures that the return you earn is
the risk-free return plus the excess return of your portfolio over the market
Rolling The Hedge Forward
bull We can use a series of futures contracts to increase the life of a hedge
bull Each time we switch from one futures contract to another we incur a type of basis risk
Simple Valuation of Futures and Forward Contracts
S0 Spot price today
F0 Futures or forward price today
T Time until delivery date
r Risk-free interest rate for maturity T
Gold An Arbitrage Opportunity
bull Suppose that
ndash The spot price of gold is US$390
ndash The quoted 1-year forward price of gold is US$425
ndash The 1-year US$ interest rate is 5 per annum
ndash No income or storage costs for gold
bull Is there an arbitrage opportunity
The Forward Price of Gold
If the spot price of gold is S and the futures price is for a contract deliverable in T years is F then
F = S (1+r )T
Where r is the 1-year (domestic currency) risk-free rate of interest
In our examples S=390 T=1 and r=005 so that
F = 390(1+005)1 = 40950
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Risk management The equity managerrsquos market risk or the bond managerrsquos interest rate risk is similar
to the farmerrsquos price risk
bull Risk transfer Derivatives provide a means for risk to be transferred from one person to some other
market participant who for a price is willing to bear it
bull Derivatives may provide financial leverage
Risk Management
bull The hedgerrsquos primary motivation is risk management
bull Someone who is bullish believes prices are going to rise
bull Someone who is bearish believes prices are going to fall
bull We can tailor our risk exposure to any points we wish along a bullish bearish sentiments of the market
Falling prices Flat market Rising prices
expected expected expected
Bearish Neutral Bullish
Increasing Bearishness Increasing Bullishness
For All Users of Derivatives
bull Risk must be quantified and risk limits set
bull Exceeding risk limits not acceptable even when profit results
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
42
bull Be diversified
bull Scenario analysis is important
Uses of Derivatives
bull Risk management
bull Income generation
bull Financial engineering
bull Writing Calls
Lecture 44
Uses of Derivatives
Income generation Some people use derivatives as a means of generating additional income from their
investment portfolio
bull Writing a covered call is a way to generate income
ndash Involves giving someone the right to purchase your stock at a set price in exchange for an up-
front fee (the option premium) that is yours to keep no matter what happens
bull Writing calls is especially popular during a flat period in the market or when prices are trending
downward
Financial Engineering
bull Financial engineering refers to the practice of using derivatives as building blocks in the creation of
some specialized product
bull Derivatives can be stable or volatile depending on how they are combined with other assets
bull Financial engineers
bull Select from a wide array of puts calls futures and other derivatives
bull Know that derivatives are neutral products (neither inherently risky nor safe)
Effective Study of Derivatives
bull All financial institutions can make some productive use of derivative assets
ndash Investment houses
ndash Asset-liability managers at banks
ndash Pension fund managers
ndash Mortgage officers
What are Options
bull Call Options
ndash A call option gives its owner the right to buy it is not a promise to buy
bull For example a store holding an item for you for a fee is a call option
bull Put Options
ndash A put option gives its owner the right to sell it is not a promise to sell
bull For example a lifetime money back guarantee policy on items sold by a company is an
embedded put option
Basic Option Characteristics
bull The option premium is the amount you pay for the option
bull Exchange-traded options are fungible
ndash For a given company all options of the same type with the same expiration and striking price are
identical
bull The striking price of an option is its predetermined transaction price
Standardized Option Characteristics
bull Expiration dates
ndash The Saturday following the third Friday of certain designated months for most options
bull Striking price
ndash The predetermined transaction price in multiples of $250 or $5 depending on current stock
price
bull Underlying Security
ndash The security the option gives you the right to buy or sell
ndash Both puts and calls are based on 100 shares of the underlying security
Where Options Come From
bull Unlike more familiar securities there is no set number of put or call options
ndash The number in existence changes every day
Some Terminology
bull Open interest
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
43
The total number of contracts outstanding
ndash Equal to number of long positions or number of short positions
bull Settlement price
The price just before the final bell each day
ndash Used for the daily settlement process
bull Volume of trading The number of trades in 1 day
bull In-the-money options have a positive cash flow if exercised immediately
ndash Call options S gtE
ndash Put options S ltE
bull Out-of-the-money options should not be exercised immediately
ndash Call options S ltE
ndash Put options S gtE
bull Intrinsic value is the value realized from immediate exercise
ndash Call options maximum (S0-E or 0)
ndash Put options maximum (E-S0 or 0)
bull Prior to option maturity option premiums exceed intrinsic value
ndash Time value =Option price - Intrinsic value
ndash =seller compensation for risk
bull Call (Put) Buyer has the right but not the obligation to purchase (sell) a fixed quantity from (to) the
seller at a fixed price before a certain date
ndash Exercise (strike) price ―fixed price
ndash Expiration (maturity) date ―certain date
bull Option premium or price paid by buyer to the seller to get the ―right
Why Options Markets
bull Financial derivative securities derive all or part of their value from another (underlying) security
bull Options are created by investors sold to other investors
bull Why trade these indirect claims
ndash Expand investment opportunities lower cost increase leverage
Why Options Are a Good Idea
bull Increased risk
bull Instantaneous information
bull Portfolio risk management
bull Risk transfer
bull Financial leverage
bull Income generation
How Options Work
bull Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)
bull Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)
bull At option maturity
ndash Option may expire worthless be exercised or be sold
Options Trading
bull Option exchanges are continuous primary and secondary markets
ndash Chicago Board Options Exchange largest
bull Standardized exercise dates exercise prices and quantities
ndash Facilitates offsetting positions through Options Clearing Corporation
bull OCC is guarantor handles deliveries
Opening and Closing Transactions
bull The first trade someone makes in a particular option is an opening transaction for that person
bull When the individual subsequently closes that position out with a second trade this latter trade is a
closing transaction
bull When someone buys an option as an opening transaction the owner of an option will ultimately do one
of three things with it
bull Sell it to someone else
bull Let it expire
bull Exercise it
bull For example buying a ticket to an athletic event
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
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httpgroupsgooglecomgroupvuzs
44
bull When someone sells an option as an opening transaction this is called writing the option
bull No matter what the owner of an option does the writer of the option keeps the option premium
that he or she received when it was sold
The Role of the Options Clearing Corporation (OCC)
bull The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the
options market
ndash It positions itself between every buyer and seller and acts as a guarantor of all option trades
ndash It sets minimum capital requirements and provides for the efficient transfer of funds among
members as gains or losses occur
Where and How Options Trade
bull Exchanges
bull Over-the-counter options
bull Standardized option characteristics
bull Other listed options
bull Trading mechanics
Exchanges
bull Major options exchanges in the US
ndash Chicago Board Options Exchange (CBOE)
ndash American Stock Exchange (AMEX)
ndash Philadelphia Stock Exchange (Philly)
ndash Pacific Stock Exchange (PSE)
bull Foreign options exchanges also exist
Over-the-Counter Options
bull With an over-the-counter option
ndash Institutions enter into ―private option arrangements with brokerage firms or other dealers
ndash The striking price life of the option and premium are negotiated between the parties involved
bull Over-the-counter options are subject to counterparty risk and are generally not fungible
Some Exotic Options
bull As-You-Like-It Option
ndash The owner can decide whether it is a put or a call by a certain date
bull Barrier Option
ndash Created or cancelled if a pre-specified price level is touched
bull Forward Start Option
ndash Paid for now with the option becoming effective at a future date
Other Listed Options
bull Long-Term Equity Anticipation Security (LEAP)
ndash Options similar to ordinary listed options except they are longer term
bull May have a life up to 39 months
Lecture 45 (Over all Revision)
1 Investing
2 Investment Alternatives
3 Category of Stocks
4 Types Of Orders
5 Types of Accounts
6 Fundamental Analysis
7 Sector Industry Analysis
8 Balance Sheet
9 Income Statement
10 Statement of Cash Flow
11 Multiples
12 Fundamental vs Technical
13 Charts
14 Basic Technical Tools
Trend Lines
Moving Averages
Price Patterns
Indicators
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)
Prepared by Humera Fazal Channab College
Short Notes FIN 630 Chapters 23-45
wwwvuzsnet
httpgroupsgooglecomgroupvuzs
45
Cycles
15 Indirect Investments Investment Companies
16 Passive Stock Strategies
17 Efficient Market Hypothesis
18 Index
19 Alternative Investments Non-marketable Financial Assets
20 Money Market Securities
21 Bond Prices
22 Bond Ratings
Investment grade securities
a Rated AAA AA A BBB
b Typically institutional investors are confined to bonds in these four categories
Speculative securities
c Rated BB B CCC C
d Significant uncertainties
e C rated bonds are not paying interest
23 Risk
24 Risk Types
25 Risk Sources
26 Portfolio Theory
27 Markowitz Diversification
28 An Efficient Portfolio
29 Capital Asset Pricing Model
30 Portfolio Choice
31 Market Portfolio
32 How Accurate Are Beta Estimates
33 Arbitrage Pricing Theory
34 Portfolio Management
35 Performance Measurement
36 What are Derivatives
37 Derivatives Instruments
38 Understanding Futures Markets
39 Participants In the Derivatives World
40 Ways Derivatives are Used
41 Using Futures Contracts
42 Speculation
43 Third Type of Trader
44 Uses of Derivatives
45 Uses of Derivatives
46 Financial Engineering
47 What are Options
48 Basic Option Characteristics
Always Remember Our Group in Your Prayers
(Humera Fazal Farhana Burhan Ayesha
Masood Shaista Zulfiqar Gill amp Naveed)